The Nilpotent Cone for Classical Lie Superalgebras
The Nilpotent Cone for Classical Lie Superalgebras
复制标题
经典李超代数的幂零锥
DOI：
10.1090/proc/15599
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发表时间：
2021
影响因子：
1
通讯作者：
Nakano, Daniel K.
中科院分区：
文献类型：
--
作者：
Jenkins, L. Andrew;Nakano, Daniel K.
本文引入了经典李超代数的幂零锥的一个类似，推广了半简单李代数的幂零锥的定义。对于一个经典的简单李超代数，用，证明了其上存在有限多轨道。随后，作者证明了dufl - serganova交换变量，，存在于任何经典单李超代数中。因此，我们的有限性结果推广和推广了dufl - serganova关于交换变项的工作。最后给出了进一步的应用。参考文献
In this paper the authors introduce an analogue of the nilpotent cone,, for a classical Lie superalgebra,, that generalizes the definition for the nilpotent cone for semisimple Lie algebras. For a classical simple Lie superalgebra,with, it is shown that there are finitely many-orbits on. Later the authors prove that the Duflo-Serganova commuting variety,, is contained infor any classical simple Lie superalgebra. Consequently, our finiteness result generalizes and extends the work of Duflo-Serganova on the commuting variety. Further applications are given at the end of the paper. References