We completely describe the decompositions (into indecomposable submodules) of the tensor products of irreducible sl(2)-modules in characteristic 3. The answer resembles analogous decompositions for the Lie superalgebra sl(1|1).

The character formula of any finite dimensional irreducible module Lλ for Lie superalgebra osp(n|2) is computed. As a by-product, the decomposition of tensor module Lλ ⊗ C n|2, where Cn|2 is the natural representation, is obtained.

We give a complete classification of infinite dimensional indecomposable weight modules over the Lie superalgebra sl(2/1). §1. Introduction Among the basic-classical Lie superalgebras classified by Kac [3], the lowest dimensional of these is the Lie superalgebra B(0, 1) or osp(1, 2), while the lowest dimensional of these which has an isotropic odd simple root is the Lie superalgebra A(1, 0) or ...

We classify nontrivial deformations of the standard embedding of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional supercircle into the Lie super-algebra of superpseudodifferential operators on the supercircle. This approach leads to the deformations of the central charge induced on K(1) by the canonical central extension of SΨDO.

We find the free field construction of basic $W$-current and screening currents for deformed $W$-superalgebra ${\cal W}_{q,t}\bigl(A(M,N)\bigr)$ associated with Lie superalgebra type $A(M,N)$. Using this construction, we introduce higher $W$-currents obtain a closed set quadratic relations among them. These are independent choice Dynkin-diagrams $A(M,N)$, though not. This allows us to define by...