Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic sub-supergroup to the category of locally finite modules of the quantum general linear supergroup. The right derived functors of this functor provides a form of D...

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.

Using Howe duality we compute explicitly Kostant-type homology groups for a wide class of representations of the infinite-dimensional Lie superalgebra b gl∞|∞ and its classical subalgebras at positive integral levels. We also obtain Kostant-type homology formulas for the Lie algebra b gl∞ at negative integral levels. We further construct resolutions in terms of generalized Verma modules for the...

One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial derivatives, connected with volume-preserving diffeomorphisms. In this paper, we determine the structure space of the divergence-free Lie algebras associated with pair...

The Lie superalgebra psl(2|2) is recognized as a quite special algebra. In mathematics, it has the vanishing Killing form and allows for three-dimensional central extension. physics, shows up symmetry of one-dimensional Hubbard model asymptotic S-matrix anti-de Sitter/conformal field theory (AdS/CFT) correspondence. this paper, we present Drinfeld realization Yangian algebra associated with cen...