A Hochschild's 6-term exact sequence for restricted Lie superalgebras

超交换代数与分次限制顶点超代数的上同调理论

A cohomology theory of supercommutative algebras and grading-restricted vertex superalgebras

本文推广黄一智的相关理论，构建分次限制顶点超代数的上同调理论，同时补充此前未明确给出的超交换结合代数上同调理论构建，为顶点超代数形变等后续研究奠基。

Simple restricted modules over the $N=1$ Ramond algebra as weak modules for vertex operator superalgebras

In the present paper, a class of new simple modules over the $N=1$ Ramond algebra are constructed, which are induced from simple modules over some finite dimensional solvable Lie superalgebras. These new modules are simple restricted modules over the $N=1$ Ramond algebra. Combined with the result in \cite{L1}, a classification of simple weak $ψ$-twisted $\bar W(0,c)$-modules under certain conditions is also given. At last, some examples of simple restricted $N=1$ Ramond modules as various versions of Whittaker modules are presented (classical Whittaker modules were studied in \cite{LPX}).

On the double of the (restricted) super Jordan plane

We consider the super Jordan plane, a braided Hopf algebra introduced--to the best of our knowledge--in works of N. Andruskiewitsch, I. Angiono, I. Heckenberger, and its restricted version in odd characteristic introduced by the same authors. We show that their Drinfeld doubles give rise naturally to Hopf superalgebras justifying a posteriori the adjective super given in their work. These Hopf superalgebras are extensions of super commutative ones by the enveloping, respectively restricted enveloping, algebra of $\mathfrak{osp}(1|2)$.

Representations of Lie Superalgebras in Prime Characteristic I

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a mixture of p-power and 2-power divisibilities of dimensions of modules. We establish the Conjecture for basic classical Lie superalgebras.

Representations of Lie superalgebras in prime characteristic III

For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of g-modules. In particular, we give a new proof of the Super Kac-Weisfeiler conjecture for basic classical Lie superalgebras. The new proof allows us to improve optimally the assumption on p. We also establish a semisimplicity criterion for the reduced enveloping superalgebras associated with semisimple p-characters for all basic classical Lie superalgebras using the t…

特征 2 与混合特征下的李超代数

Lie superalgebras in characteristic 2 and mixed characteristic

本文统一了特征 2 下两种李超代数定义，证明其普通与受限版本的 PBW 定理，并提出混合李超代数以研究向特征零的提升与形变。