مواقع التدريسيينجامعة الكوفة
Dr Hasan Mohammed Ali Saeed Shlaka
Assistant Professor

Dr Hasan Mohammed Ali Saeed Shlaka

Computer Science and Mathematics Mathematics
[email protected]
النسخة العربية
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About

I have awarded a degree of Mathematics PhD from Department of Mathematics at University of Leicester on June 26th, 2018 under the supervision of Dr Alexander Baranov. My research interests Lie and associative Algebras and representation theory. Prior to that I have obtained a degree of Mathematics MSc. From the Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa on November 20th, 2012, and a degree of Mathematics BSc. From the Department of Mathematics, Faculty of Science, University of Kufa on July, 27th 2007.
I have been elected to be an associate member of the London mathematical Society (LMS) on November 1st, 2016.
Recently, I have been awarded a grant of £3,000 from the London Mathematical Society towards travel, accommodation and subsistence, to visit the United Kingdom, in order to collaborate, in mathematical research, with Dr Alexander Baranov at the University of Leicester, from May 12th to June 20th 2022.

Grants obtained
Grant reference 52102
Name of Funding Organization: The London Mathematical Society
Amount awarded: £3000
Period of Grant Award: From May 12th until June 12th 2022
Title of Project: Collaboration in mathematical research with Dr Alexander Baranov at the University of Leicester.

Talks giving:
• Faculty workshop for undergraduate students, November 22nd 2022, “How can you write a successful CV to obtain a Job”, Faculty of Computer Science and Mathematics.
• Faculty Workshop, November 11th 2022, “Using LYX Software to write Lecture notes, Research papers, Theses and Dissertations”, Faculty of Computer Science and Mathematics.
• 51st Annual Iranian Mathematics Conference, February 15−20 2021, “Simple Associative Algebras and their Corresponding finitary Simple Lie Algebras”.
• The Fifth international conference of the Iraqi Al-Khwarizmi Association, April 14-15th 2020, “Locally Finite Associative Algebras and Their Lie Subalgebras”
• The scientific symposium, The Iraqi Al-Khwarizmi Association in cooperation with the University of Al-Muthanna College of Science, Iraq, November 14-15th 2018, “Updating the curriculum of some subjects in Mathematics”
• LMS Summer Graduate Students Meeting, London Mathematical Society, June 29th 2018, "Classical Simple Lie Algebras".
• Young Mathematician Colloquium, University of Birmingham, April 18th, 2018, "Jordan-Lie Inner Ideals of Associative Algebras".
• PhD seminar, University of Leicester, December 13th, 2017, "Inner Ideals of Finite Dimensional simple Lie Algebras".
• PhD seminar, University of Leicester, November 16th, 2016, "The Structure of the Lie algebras that obtained from associative algebras".
Conferences and workshops:
1- The Fifth international conference of the Iraqi Al-Khwarizmi Association, April 14-15th 2020 (the conference postpone due to the quarantine).
2- The Seventh international conference on Performance, University of Kufa, March 27-28th 2019.
3- Workshop on Non-Associative Algebras and Applications, University of Lancaster, July 9th-13th, 2018
4- LMS Summer Graduate Students Meeting, London Mathematical Society, June 29th 2018
5- Artin 53rd meeting, University of Manchester, April 26-27th, 2018.
6- Young Mathematician Colloqium, University of Birmingham, April 18th, 2018.
7- Artin 52nd meeting, University of Aberdeen, March 21-23rd, 2018.
8- Workshop on Lie Theory, Representation Theory and Algebraic Group, University of Manchester, September 11-14, 2017.
9- Seventy-eight BLOC meeting, University of Oxford, 23-24, August, 2017.
10- LMS graduate student meeting, London Mathematical Society, June 30, 2017.
11- Seventy-seventh BLOC meeting, University of Leicester, June 6, 2017.
12- Sventy-six BLOC meeting, City University of London, March 8, 2017.
13- LMS graduate student meeting, London Mathematical Society, November 11, 2016.
14- Conference on Representation Theory and physics, University of Leeds, July 18-22, 2016.
15- Seventy-fourth BLOC meeting, University of Leicester, July 1, 2016.
16- Young Mathematicians Colloquium University of Birmingham, April 20, 2016.
17- Seventy-second BLOC meeting, University of Bristol, March 24, 2016.
18- Workshop on Cluster Algebras and Finite Dimensional Algebras, University of Leicester, June 3-5, 2015.

International training courses that I have participated in:
1- “How to Succeed at: Writing Applications”, three weeks online course, the University of Sheffield, June 9nd-29nd, 2023.
2- “Focusing On…Classroom Management”, University of Leicester, March 2018.

3- “Focusing On…Learning Theories”, University of Leicester, February 2018.

4- “Preparing to teach in higher education”, University of Leicester, November 2016.

Teaching experience:
1- Foundations of Mathematics, 1st year Undergraduate Math students, Faculty of Computer Science and Maths, Semester II, 2022-2023.
2- Mathematical Analysis, 3rd year Undergraduate Math students, Faculty of Education For Girls, Semester I and II, 2022-2023.
3- Real Analysis, 3rd year Undergraduate Math students, Faculty of Computer Science and Mathematics, Semester I, 2022-2023.
4- Mathematical Analysis II, 3rd year Undergraduate Math students, Faculty of Computer Science and Mathematics, Semester II, 2021-2022.
5- Real Analysis, 3rd year Undergraduate Mathematics students, Faculty of Computer Science and Mathematics, Semester I, 2021-2022.
6- Lie Algebra, Postgraduate Msc. Mathematics students, Faculty of Computer Science and Mathematics, Semester II, 2020-2021.
7- Mathematical Analysis II, 3rd year Undergraduate Math students, Faculty of Computer Science and Mathematics, Semester II, 2020-2021.
8- Mathematical Analysis, 3rd year Undergraduate Math students, Faculty of Education, Semesters I and II, 2021-2022.
9- Lie Algebra, Postgraduate Msc. Math students, Faculty of Computer Science and Mathematics, Semester II, 2020-2021.
10- Mathematical Analysis II, 3rd year Undergraduate Mathematics students, Faculty of Computer Science and Mathematics, Semester II, 2020-2021.
11- Advanced Abstract Algebra, Postgraduate Msc. Math students, Faculty of Computer Science and Mathematics, Semester I, 2020-2021.
12- Advanced Abstract Algebra, Postgraduate MSc Math students, Faculty of Computer Science and Mathematics, Semester I, 2020-2021.
13- Mathematical Analysis I, 3rd year Undergraduate Math students, Faculty of Computer Science and Mathematics, Semester I, 2020-2021.
14- Mathematical Analysis II, 3rd year Undergraduate Math students, Faculty of Computer Science and Mathematics, Semester II, 2019-2020.
15- Engineering Mathematics II, 2nd year Undergraduate Chemical Engineering Students, Faculty of Engineering, University of Kufa, Semester II, 2019-2020.
16- Mathematical Analysis I, 3rd year Undergraduate Math students, Faculty of Computer Science and Mathematics, Semester I, 2019-2020.
17- Engineering Mathematics I, 2nd year Undergraduate Chemical Engineering Students, Faculty of Engineering, University of Kufa, Semester I, 2019-2020.
18- Linear Algebra II, 3rd year Undergraduate Mathematical Science students, Faculty of Computer Science and Mathematics, University of Kufa, 2018-2019.
19- Mathematics I, 1st year Undergraduate Material Engineering students, Faculty of Engineering, University of Kufa, 2018-2019.
20- Mathematics II, 1st year Undergraduate Material Engineering students, Faculty of Engineering, University of Kufa, 2018-2019.
21- Engineering Mathematics, 2nd year Undergraduate Telecommunication Engineering students, Faculty of Engineering, University of Kufa, 2012-2013.
22- Engineering Mathematics, 2nd year Undergraduate Material Engineering Students, Faculty of Engineering, University Kufa, 2012-2013.

Teaching experience during my PhD at the University of Leicester UK:
I have taught feedback and supervision the following classes:
1- Linear Algebra I, first year undergraduate students, University of Leicester, 2016-2017.
2- Linear Algebra II, first year undergraduate math students, University of Leicester, 2016-2017.
3- Linear Algebra II, first year undergraduate math students, University of Leicester, 2017-2018.
4- Calculus and Analysis II, first year undergraduate students, University of Leicester, 2017-2018.
5- Lineal Algebra I, first year undergraduate math students, University of Leicester, 2017-2018.
6- Calculus and Analysis I, first year undergraduate students, University of Leicester 2017-2018.

Research Interests

4
AlgebraAssociative algebrasNon-Associative AlgebrasRepresentation Theory

Publications

14
2023

The finitary symplectic and finitary orthogonal Lie sub-algebras of associative algebras

AuthorsHasan M. Shlaka
JournalAIP Conference Publishing, .
Abstract

Let

View Paper
2023

Inner ideals of the special linear lie algebras of associative simple finite dimensional algebras

AuthorsHasan M. Shlaka, Durgham A. Mousa
JournalAIP Conference Proceedings
Abstract

In this paper, we discuss and study the structure of inner ideals of the special linear Lie algebras of associative simple algebras. We prove that if A is an associative finite dimensional simple algebra over algebraically closed fields of positive characteristic, then every inner ideal of regular type of [A, A] is generated by a pair of idempotents.

View Paper
2023

Generalization of Jordan-Lie of Finite Dimensional Associative Algebras

AuthorsHasan M.Shlaka
JournalJournal of Algebra and Its Applications
Abstract

We generalize Baranov and Shlaka’s results about bar-minimal Jordan-Lie and regular inner ideals of finite dimensional associative algebras. Let A be a finite dimensional 1 -perfect associative algebras A over an algebraically closed field F of arbitrary characteristic p and let A′ be a subalgebra of A . We prove that for any bar-minimal Jordan-Lie inner ideal B′ a A′ , there is a bar-minimal Jordan-Lie inner ideal of A that contains B′ and if B′ is regular, then is a regular inner ideal of A that contains B′ . We also prove that for any strict orthogonal pair (e′,f′) in A′ , there is a strict orthogonal idempotent pair (e,f) in A such that e′A′f′⊆eAf .

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2022

Abelian Non Jordan-Lie Inner Ideals of the Orthogonal Finite Dimensional Lie Algebras

AuthorsHasan M. Shlaka, Falah S. Kareem
JournalJournal of Discrete Mathematical Sciences and Cryptography
Abstract

Let A associative algebra (finite dimensional over ) of any characteristic with involution * and let K = skew(A) = {a ∈ A|a* = -a} be its corresponding sub-algebra under the Lie product [a, b] = ab - ba for all a, b ∈ A. If A = End V for some finite dimensional vector space over and * is an adjoint involution with a symmetric non-alternating bilinear form on V, then * is said to be orthogonal. In this paper, abelian inner ideals which are non Jordan-Lie of such Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that every abelian inner ideal which is non Jordan-Lie B of K can be expressed as B = {v, H⊥}, where v is an isotropic vector of a hyperbolic plane H ⊆ V and H⊥ is the orthogonal subspace of H.

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2022

Inner Ideals of The Symplectic Simple Lie Algebra

AuthorsFalah S. Kareem, Hasan M. Shlaka
JournalJournal of Physics Conference Series, IOP Science.
Abstract

Let A be an associative algebra over a field Bbb F of any characteristic with involution and let K = skew (A) = { a ∈ A | a* = − a} be its corresponding sub-algebra under the Lie product [a, b] = ab − ba for all a, b ∈ A. In this paper, inner ideals of such Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that for every Jordan-Lie inner ideal of K, one can find an idempotent e ∈ A such that this inner ideal may be written in the form eK e*. It is also proved inner ideals of such Lie algebras are regular.

View Paper
2020

Jordan-Lie inner ideals of finite dimensional associative algebras

AuthorsDr Alexander Baranov , Dr Hasan Mohammed Ali Saeed Shlaka
JournalJournal of Pure and Applied Algebra
Abstract

We study Jordan-Lie inner ideals of finite dimensional associative algebras and the corresponding Lie algebras and show that they admit Levi decompositions. Moreover, we classify Jordan-Lie inner ideals satisfying a certain minimality condition and show that they are generated by pairs of idempotents.

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2020

Locally Finite Associative Algebras and Their Lie Subalgebras

AuthorsDr Hasan Mohammed Ali Saeed Shlaka
JournalJournal of Physics: Conference Series
Abstract

An infinite dimensional associative algebra ${\mathcal{A}}$ ${\mathcal{A}}$ over a field ${\mathbb{F}}$ is called locally finite associative algebra if every finite set of elements is contained in a finite dimensional subalgebra of ${\mathcal{A}}$. Given any associative algebra ${\mathcal{A}}$ over field ${\mathbb{F}}$ of any characteristic. Consider a new multiplication on ${\mathcal{A}}$ called the Lie multiplication which defined by [a, b] = ab − ba for all a, b ∈ A, where ab is the associative multiplication in ${\mathcal{A}}$. Then L = ${\mathcal{A}}$(−) together with the Lie multiplication form a Lie subalgebra of ${\mathcal{A}}$. It is natural to expect that the structures of L and ${\mathcal{A}}$ are connected closely. In this paper, we study and discuss the structure of infinite dimensional locally finite Lie and associative algebras. The relation between them, their ideals and their inner ideals is considered. A brief discussion of the simple associative algebras and simple Lie algebras is also be provided.

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2020

Jordan-Lie inner ideals of the finite dimensional associative algebras

AuthorsAlexander Baranov, Hasan M. Shlaka
Journal Journal of Pure and Applied Algebra, ELSEVIER
Abstract

We study Jordan-Lie inner ideals of finite dimensional associative algebras and the corresponding Lie algebras and prove that they admit Levi decompositions. Moreover, we classify Jordan-Lie inner ideals satisfying a certain minimality condition and show that they are generated by pairs of idempotents.

View Paper
2020

Locally Finite Associative Algebras and Their Lie Subalgebras

AuthorsHasan M. Shlaka
JournalJournal of Physics: Conference Series IOP Science
Abstract

An infinite dimensional associative algebra ${\mathcal{A}}$ ${\mathcal{A}}$ over a field ${\mathbb{F}}$ is called locally finite associative algebra if every finite set of elements is contained in a finite dimensional subalgebra of ${\mathcal{A}}$. Given any associative algebra ${\mathcal{A}}$ over field ${\mathbb{F}}$ of any characteristic. Consider a new multiplication on ${\mathcal{A}}$ called the Lie multiplication which defined by [a, b] = ab − ba for all a, b ∈ A, where ab is the associative multiplication in ${\mathcal{A}}$. Then L = ${\mathcal{A}}$(−) together with the Lie multiplication form a Lie subalgebra of ${\mathcal{A}}$. It is natural to expect that the structures of L and ${\mathcal{A}}$ are connected closely. In this paper, we study and discuss the structure of infinite dimensional locally finite Lie and associative algebras. The relation between them, their ideals and their inner ideals is considered. A brief discussion of the simple associative algebras and simple Lie algebras is also be provided.

View Paper
2018

- Jordan-Lie inner ideals of finite dimensional associative algebras

AuthorsHasan M. Shlaka
JournalUniversity of Leicester
Abstract

A subspace B of a Lie algebra L is said to be an inner ideal if [B, [B,L]] ⊆ B. Suppose that L is a Lie subalgebra of an associative algebra A. Then an inner ideal B of L is said to be Jordan-Lie if B2 = 0. In this thesis, we study Jordan-Lie inner ideals of finite dimensional associative algebras (with involution) and their corresponding Lie algebras over an algebraically closed field F of characteristic not 2 or 3. Let A be a finite dimensional associative algebra over F. Recall that A becomes a Lie algebra A(-) under the Lie bracket defined by [x,y] = xy - yx for all x,y ∈ A. Put A(0) = A(-) and A(k) = [A(k-1),A(k-1)] for all k ≥ 1. Let L be the Lie algebra A(k) (k ≥ 0). In the first half of this thesis, we prove that every Jordan-Lie inner ideal of L admits Levi decomposition. We get full classification of Jordan-Lie inner ideals of L satisfying a certain minimality condition. In the second half of this thesis, we study Jordan-Lie inner ideals of Lie subalgebras of finite dimensional associative algebras with involution. Let A be a finite dimensional associative algebra over F with involution * and let K(1) be the derived Lie subalgebra of the Lie algebra K of the skew-symmetric elements of A with respect to *. We classify * -regular inner ideals of K and K(1) satisfying a certain minimality condition and show that every bar-minimal * -regular inner ideal of K or K(1) is of the form eKe* for some idempotent e in A with e*e = 0. Finally, we study Jordan-Lie inner ideals of K(1) in the case when A does not have “small” quotients and show that they admit *-invariant Levi decomposition.

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2018

Wedderburn–Malcev decomposition of one-sided ideals of finite dimensional algebras

AuthorsAlexander Baranov, Andrey Mudrov and Hasan Shlaka
JournalCommunications in Algebra
Abstract

Let A be a finite dimensional associative algebra over a perfect field and let R be the radical of A. We show that for every one-sided ideal I of A there exists a semisimple subalgebra S of A such that I=IS⊕IR where IS = I∩S and IR = I∩R.

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2012

The Closed Ideal With Respect To an Element Of a BH-Algebra

AuthorsHusein Hadi Abbass, HASAN SHLAKA
JournalThe 4th International Scientific Conference for College of Computer Science and Mathematics Al-Qadis
Abstract

In this paper, we generalize some basic concepts to a BH-algebra, we find the relation between the notion of an associative BH-algebra and a Group of abstract algebra and we define the notion of a closed ideal with respect to an element of a BH-algebra which is a generalization of the notion of a closed ideal with respect to an element of a BCH-algebra.

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2011

The Fuzzy Closed BH-Algebra With Respect To an Element ‫

AuthorsHusein Hadi Abbass, Hasan Shlaka
JournalThe Proceedings of the 4th Conference of College of Education ,for Pure Sciences
Abstract

In this paper, we define the concepts of a fuzzy closed ideal with respect to an element of a BH-algebra and a fuzzy closed BH-algebra with respect to an element of BH-algebra. We stated and proved some theorems which determine the relation between these notion and the notions of fuzzy ideals in a BH-algebra.

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2011

ON CLOSED BCH-ALGEBRA WITH RESPECT TO AN ELEMENT OF A BCH-ALGEBRA

AuthorsHusein Hadi Abbass, Hasan Shlaka
JournalJournal of Kufa for Mathematics and Computer
Abstract

In this paper, we define the concepts of a closed ideal with respect to an element of a BCH-algebra and a closed BCH-algebra with respect to an element of BCH-algebra . We stated and proved some theorems which determine the relationship between these notion and the notions of some ideals of a BCH-algebra.

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Lectures

6

News & Announcements

1
Announcements 2018-09-19

Scientific writing program LYX

For all of the researcher who would like to write their research papers in Latex instead of the Microsoft word program. My suggestion is to use LYX instead of LATEX, as the LYX is easy to be used like Microsoft word and free to be downloaded from the internet. :You can download the program by using the following link https://www.lyx.org/Download For more information about this program, please, email me. Thanks

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