Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras
Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie s...
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De Gruyter
2019-11-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2019-0117 |
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doaj-f5ca0aaad24647b6835f35e474d573fb2021-09-06T19:20:11ZengDe GruyterOpen Mathematics2391-54552019-11-011711381139110.1515/math-2019-0117math-2019-0117Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebrasZheng Keli0Zhang Yongzheng1Department of Mathematics, Northeast Forestry University, Harbin, 150040, P.R. ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P.R. ChinaLet 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.https://doi.org/10.1515/math-2019-0117modular lie superalgebragraded moduleirreducibilityhighest weight17b1017b5017b70 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zheng Keli Zhang Yongzheng |
| spellingShingle |
Zheng Keli Zhang Yongzheng Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras Open Mathematics modular lie superalgebra graded module irreducibility highest weight 17b10 17b50 17b70 |
| author_facet |
Zheng Keli Zhang Yongzheng |
| author_sort |
Zheng Keli |
| title |
Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras |
| title_short |
Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras |
| title_full |
Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras |
| title_fullStr |
Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras |
| title_full_unstemmed |
Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras |
| title_sort |
irreducible modules with highest weight vectors over modular witt and special lie superalgebras |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2019-11-01 |
| description |
Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules. |
| topic |
modular lie superalgebra graded module irreducibility highest weight 17b10 17b50 17b70 |
| url |
https://doi.org/10.1515/math-2019-0117 |
| work_keys_str_mv |
AT zhengkeli irreduciblemoduleswithhighestweightvectorsovermodularwittandspecialliesuperalgebras AT zhangyongzheng irreduciblemoduleswithhighestweightvectorsovermodularwittandspecialliesuperalgebras |
| _version_ |
1717777129825894400 |