Finite W-superalgebras for basic Lie superalgebras
Finite W-superalgebras for basic Lie superalgebras
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DOI：
10.1016/j.jalgebra.2015.04.034
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Yang Zeng;B. Shu
中科院分区：
文献类型：
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作者：
Yang Zeng;B. Shu
考虑复数域F= C和复数域F= k上的基本李超代数gF =（gF）0 <$+（gF）1 <$伴随有幂零元e∈（gF）0 <$的有限W-超代数U（gF，e）是正特征的代数闭域.本文主要给出U（gF，e）的PBW定理.这样就可以很好地理解U（g F，e）的构造，与有限W-代数相比，U（g F，e）的构造根据dim g F（− 1）1 <$的奇偶性分为两种情况。这一观察将是我们对基本李超代数的模表示的超Kac-Weisfeiler性质的维数下界的研究工作的基础（参见。[43，§ 7-§ 9]）。
We consider the finite W-superalgebra U (g F, e) for a basic Lie superalgebra g F=(g F) 0¯+(g F) 1¯ associated with a nilpotent element e∈(g F) 0¯ both over the field of complex numbers F= C and over F= k an algebraically closed field of positive characteristic. In this paper, we mainly present the PBW theorem for U (g F, e). Then the construction of U (g F, e) can be understood well, which in contrast with finite W-algebras, is divided into two cases in virtue of the parity of dim g F (− 1) 1¯. This observation will be a basis of our sequent work on the dimensional lower bounds in the super Kac–Weisfeiler property of modular representations of basic Lie superalgebras (cf.[43, § 7–§ 9]).