A New Algorithm for Computing Cohomologies of Lie Superalgebras

Abstract

In this paper two versions of a new algorithm for computing cohomologies of Lie (super)algebras are described. The algorithm is based on splitting the full cochain complex into smaller subcomplexes. This approach makes the computation essentially more efficient since in most cases the dimensions of full cochain spaces included in the complexes are very high and these high-dimensional spaces can be divided into much smaller subspaces. Examples illustrating the work of the algorithm are given.