Annihilation Theorem and Separation Theorem for basic classical Lie superalgebras

The Annihilation theorem for the completely reducible Lie superalgebras

A well known theorem of Duflo claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is generated by its intersection with the centre. For a Lie superalgebra this result fails to be true. For instance, in the case of the orthosymplectic Lie superalgebra osp(1,2), Pinczon gave in [Pi] an example of a Verma module whose annihilator is not generated by its intersection with the centre of universal enveloping algebra. More generally, Musson produced in [Mu1] a family of such "singular" Verma modules for osp(1,2l) cases. In this article we give a…

基于新李超代数的简单受限模块

Simple restricted modules over a new Lie superalgebra extended by the Ovsienko--Roger algebra

本文介绍了基于新李超代数的简单受限模块构造，并研究了其广义Verma模的分类与可约性。