• 18 January 2023
• 2435

Scientific research on mathematics was conducted

Brief information about the project

Theme: AR08855935 "Сlassical algebras are in useful characteristics: simple modules and cohomology".

Budget program: 217 "Development of science".

Subprogram: 102 " Grant funding of scientific research".

Priority: " Scientific research in the field of natural sciences".

Scientific supervisor: c.ph.-m.s., Associate Professor Sh.Sh. Ibraev.

Relevance: the study of their simple representations and the study of the cohomology of simple modules of modularized classical algebra is one of the key tasks of the theory of modularized algebra. At the present moment, the full description of simple reduced representations received only for classically modulated algebra of small ranks, such as algebra of classicized Type A cohomology of simple modules of full description only for three-dimensional classicized algebra of type in the public service in addition, the Ministry of education and science of the Republic of Kazakhstan informed about the implementation of the program of the first president of the Republic of Kazakhstan-Elbasy. Therefore, in the study of cohomology of simple modules, a special importance is represented by a full study of cohomology of small class algebra, a three-dimensional class algebra of the type, as well as a study of cohomology of simple modules, formal characteristics and property of which can be explained with providing accessible tools for studying the theory of presentation. Scientific interests also represent their own, not studied, simple, well-defined representations of classically modulated algebra.

The purpose of the project is to study the bounded and ordinary cohomology of simple modules of classical Lie algebras over an algebraically closed field of positive characteristic whose higher weights belong to alcoves located along and near the walls of dominant Weyl chambers. It is necessary to study the relationship between reduced and specific cohomology of algebra, and their relationship with corresponding cohomology of algebraic groups of studied algebra.

Expected results:

1) the description of simple modules of classical algebra is based on the algebraic field of useful characteristics of the old world, which is headed by alcoves, expanded vents and blizi stands of the dominant Chamber of the Valley.

2) full description of the reduced cohomology of classically modular algebra with coefficients in simple modularies, determined in the task 1).

3) full identification of general cohomology of classically modular algebra with coefficients in simple modularies, determined in the task 1), and identification of cohomology of algebra of type .

4) construction of formulas and documentation and distribution between local and limited cohomology.

5) construction of formulas and calculations and development between local and limited cohomology of necessary and sufficient conditions of isomorphism of cohomology of simple modules of higher order of algebra and corresponding cohomology of their algebraic groups.

Received results:

- a full description of simple modules of classical algebra is given in the algebraic field of full-fledged characters of the old world, which are headed by alcoves, expanded vents and blizi stands of the dominant Chamber of the Valley;

- full cohomology of classically modular algebra with coefficients in simple modularies, studied in advance at the research stage, cohomology of algebra Lie type ;

- the construction of formulas and documentation on the connection between large and small cohomology for simple modules has been completed;

- the necessary and sufficient conditions of isomorphism of cohomology of simple modules are more high-order algebra and corresponding cohomology of their algebraic groups. The study topic "Аlgebra, their presentation and cohomology"was published.

Methods of study - the study of methods of theory of representation of groups and theory of representation of algebra, as well as modern methods of homological algebra, based on the use of their current and spectral pastes.

Scientific results will be presented by specialists in the theory of algebra Lie, theory of superalgebra Lie, theory of non-associative algebra, theory group, as well as specialists in the field of science, such as geometry, physics, biology and etc.

Research Group:

1) Sherali Shapatayevich Ibraev, scientific director.

Scopus Author ID: 8382250800 (https://www.scopus.com/authid/detail.uri?origin=resultslist&authorId=8382250800&zone=),

Web of Science ResearcherID: AAZ-8073-2021 (https://publons.com/researcher/4694905/sherali-ibraev/)

ORCID: 0000-0003-4844-5001 (https://orcid.org/0000-0003-4844-5001)

2) Boranbay Esmakhanbaevich Turbaev, member of the research group.

ORCID: 0000-0001-9031-2339 (https://orcid.org/0000-0001-9031-2339)

3) Dzhumadildaev Askar Serkulovich, member of the research group.

4) Seitmuratov Angysyn Zhasaralovich, member of the research group.

Scopus Author ID: 56088671300

(https://www.scopus.com/authid/detail.uri?origin=resultslist&authorId=56088671300&zone=)

Web of Science ResearcherID: ABC-4209-2020

 (https://publons.com/researcher/3983603/seitmuratov-angysyn/)

ORCID: 0000-0002-9622-9584 (https://orcid.org/0000-0002-9622-9584)

5) Menlikhozhaeva Saulesh Koilybayevna, member of the research group.

ORCID: 0000-0002-6631-7145 (https://orcid.org/0000-0002-6631-7145)

6) Larisa Sagizhanovna Kainbaeva, member of the research group.

Web of Science ResearcherID: Q-1831-2017  (https://publons.com/researcher/2042630//)

ORCID: 0000-0002-2927-6575 (https://orcid.org/0000-0002-2927-6575)

7) Ibraeva Anar Abdukarimovna, member of the research group.

ORCID: 0000-0003-4501-5997 (https://orcid.org/0000-0003-4501-5997)

8) Yeshmurat Gulnur Kuanyshkyzy, a member of the research group, a young student.

ORCID: 0000-0002-3275-6457 (https://orcid.org/0000-0002-3275-6457)

9) Shapetov Bibarys Melsuly, a member of the research group, young Scientist.

10) Ganiulla Aliya Ganiullakyzy, member of the research group, young Scientist.

More published works on research results

Results of research published 6 Articles, 3 of which have a percentile on CiteScore in the base Scopus not mine 50:

1 Ibraev Sh.Sh., Turbayev B.E. Cohomology for the Lie algebra of type  over a field of characteristic 2 // Siberian Electronic Mathematical Reports. – 2021 – Vol.18, No 2   –   P.729-739. Scopus: percentile 32, quartile SJR Category Q2 (2020).

2  Ibrayeva, A.A., Ibraev Sh.Sh, Yeshmurat G.K. Cohomology of simple modules for  in characteristic 3 // Bulletin of the Karaganda University. Mathematics Series. – 2021. – 3(103). –  P.36-43. recommended Coxon, enters the web of Science database (without quartile).

3 Ibrayev Sh.Sh., Seitmuratov A.Zh. Kainbayeva L.S.  On simple modules with singular highest weights for // Vestnik Kargu. Series. Matem. – №1(105). - 2022. - P. 52-65.recommended Coxon, enters the web of Science database (without quartile).

4 Ibrayev Sh.Sh. Cohomology of  and  with Coefficients in Simple Modules and Weyl Modules in Positive Characteristics. – SIGMA. – 2022. V. 18. –  026, 17 pages. https://doi.org/10.3842/SIGMA.2022.026 Scopus: percentile 60 (2021).

5 Ibrayev Sh.Sh., Kainbayeva L.S., Menlikhozhayeva S.K. On Cohomology of Simple Modules for Modular Classical Lie Algebras. – Axioms.  2022. – V. 11, 78. https://doi.org/10.3390/axioms11020078 Scopus: percentile 87 (2021).

6 Ibrayev Sh.Sh., Kainbayeva L.S., Seitmuratov A.Zh. On Restricted Cohomology of Modular Classical Lie Algebras and Their Applications. – Mathematics. – 2022. - V. 10(10), 1680. https://doi.org/10.3390/math10101680 Scopus: percentile 86 (2021).

The results of the research were published in the 4th International (in Kazakhstan) and in the same Republican Conference:

1 Ibraev Sh.Sh., Kainbaeva L. S. on the cohomology of simple modules of classical modular algebra Lie // thesis of the documents of the traditional international April mathematical conference on the day of the first scientific day of the Republic of Kazakhstan, dedicated to the 75th anniversary of the Academy of Sciences of the Republic of Kazakhstan T. Sh.Kalmenova.  – 2021, April 5-8, IMM KN Mon RK, Almaty. – P. 115-116.

2 Ibraev Sh.Sh., Turbayev B. E., Ibraeva A. A. cohomology of algebra is a type of small character // international scientific and practical conference "Problems of modern fundamental and Applied Mathematics", Moscow State University named after Lomonosova, Kazakhstan Branch, Library of the first president of the Republic of Kazakhstan-Elbasy, June 4 2021, Nur – Sultan. – P. 24 – 26.

3 Ibraev Sh. Sh.on the presentations of special line groups with single senior leaders // the second scientific conference of mathematicians of Kazakhstan "Actual problems of mathematics", the international Kazakh-Turkish university named after Khoja Akhmet Yasavi, IMM KN Mon RK, Turkestan, 24-28 May 2021. The document was published in the Bulletin of the MKTU named after H. A. Yasavi. –  2021. – 1(16). –  P.17-26.

4 Ibraev Sh. Sh. on basic and reduced cohomology classically modularized algebra Lie / / thesis of the documents of the Traditionalist international April mathematical conference in the past day of scientific workers of the Republic of Kazakhstan. – 2022, April 6-8, IMM KN Mon RK, Almaty. – P. 115-116.

5 Ibraev Sh.Sh., Seitmuratov A. Zh.cohomology of Algebra I type and their orientation // materials of the international scientific conference, dedicated to the 80th anniversary of Professor T. G. Mustafina "Actual tasks of Mathematics, Mechanics and computer science", Karaganda university named after E. A. Buketova, 8-9 September 2022, Karaganda.  – P. 24-266.

One educational message in Kazakh language:

1 Zhumadildaev A. S., Ibraev Sh.Sh. lie algebras, their representations and cohomologies. - Kyzylorda.: Cheese Satisfaction, 2022. – 291 P.