Cohomology of simple modules for sl3(k) in characteristic 3
In this paper we calculate cohomology of a classical Lie algebra of type A2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. To describe their structure we will consider them as modules over an algebraic group SL3(k). In the case of characteristic p...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2021-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2021-103-3/4.pdf |
| _version_ | 1797686737449779200 |
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| author | A.A. Ibrayeva |
| author_facet | A.A. Ibrayeva |
| author_sort | A.A. Ibrayeva |
| collection | DOAJ |
| description | In this paper we calculate cohomology of a classical Lie algebra of type A2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. To describe their structure we will consider them as modules over an algebraic group SL3(k). In the case of characteristic p = 3, there are only two peculiar simple modules: a simple that module isomorphic to the quotient module of the adjoint module by the center, and a one-dimensional trivial module. The results on the cohomology of simple nontrivial module are used for calculating the cohomology of the adjoint module. We also calculate cohomology of the simple quotient algebra Lie of A2 by the center. |
| first_indexed | 2024-03-12T01:10:12Z |
| format | Article |
| id | doaj.art-d40e68ed4b03404e9bec89d1d6f41ec7 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:10:12Z |
| publishDate | 2021-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-d40e68ed4b03404e9bec89d1d6f41ec72023-09-14T06:33:42ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-09-011033364310.31489/2021M3/36-43Cohomology of simple modules for sl3(k) in characteristic 3A.A. Ibrayeva In this paper we calculate cohomology of a classical Lie algebra of type A2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. To describe their structure we will consider them as modules over an algebraic group SL3(k). In the case of characteristic p = 3, there are only two peculiar simple modules: a simple that module isomorphic to the quotient module of the adjoint module by the center, and a one-dimensional trivial module. The results on the cohomology of simple nontrivial module are used for calculating the cohomology of the adjoint module. We also calculate cohomology of the simple quotient algebra Lie of A2 by the center.https://mathematics-vestnik.ksu.kz/apart/2021-103-3/4.pdf |
| spellingShingle | A.A. Ibrayeva Cohomology of simple modules for sl3(k) in characteristic 3 Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Cohomology of simple modules for sl3(k) in characteristic 3 |
| title_full | Cohomology of simple modules for sl3(k) in characteristic 3 |
| title_fullStr | Cohomology of simple modules for sl3(k) in characteristic 3 |
| title_full_unstemmed | Cohomology of simple modules for sl3(k) in characteristic 3 |
| title_short | Cohomology of simple modules for sl3(k) in characteristic 3 |
| title_sort | cohomology of simple modules for sl3 k in characteristic 3 |
| url | https://mathematics-vestnik.ksu.kz/apart/2021-103-3/4.pdf |
| work_keys_str_mv | AT aaibrayeva cohomologyofsimplemodulesforsl3kincharacteristic3 |