A program for constructing finitely presented Lie algebras and superalgebras

The purpose of this paper is to describe a C program FPLSA for investigating finitely presented Lie algebras and superalgebras. The underlying algorithm is based on constructing the complete set of relations called also standard basis or Grِbner basis of ideal of free Lie (super) algebra generated by the input set of relations. The program may be used, in particular, to compute the Lie (super) algebra basis elements and its structure constants, to classify the finitely presented algebras depending on the values of parameters in the relations, and to construct the Hilbert series. These problems are illustrated by examples.