Simple supermodules over lie superalgebras

Chih Whi Chen, Volodymyr Mazorchuk

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)

摘要

We show that, for many Lie superalgebras admitting a compatible Z-grading, the Kac induction functor gives rise to a bijection between simple supermodules over a Lie superalgebra and simple supermodules over the even part of this Lie superalgebra. This reduces the classification problem for the former to the one for the latter. Our result applies to all classical Lie superalgebras of type I, in particular, to the general linear Lie superalgebra gl(m|n). In the latter case we also show that the rough structure of simple gl(m|n)-supermodules and also that of Kac supermodules depends only on the annihilator of the gl(m) ☉ gl(n)-input and hence can be computed using the combinatorics of BGG category O.

原文???core.languages.en_GB???
頁(從 - 到)899-921
頁數23
期刊Transactions of the American Mathematical Society
374
發行號2
DOIs
出版狀態已出版 - 2月 2021

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