Computation of cohomology of Lie (super)algebra: algorithm, implementation and new results

A new algorithmic approach to computation of cohomologies of Lie (super)algebras is described briefly. This approach, based on splitting the full cochain complex into “minimal” subcomplexes, is implemented in the C language. The results of computing the cohomology in the trivial module for the Lie superalgebra SLe(2) are presented. This superalgebra, being an odd counterpart to the Lie algebras of Poisson and Hamilton vector fields, is concerned with the Batalin–Vilkovisky formalism.