Simple supermodules over lie superalgebras

Chih Whi Chen, Volodymyr Mazorchuk

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??? 899-921 23 Transactions of the American Mathematical Society 374 2 https://doi.org/10.1090/tran/8303 已出版 - 2月 2021