Lie Algebras and Superalgebras Defined by a Finite Number of Relations: Computer Analysis

DOI

10.2991/jnmp.1995.2.3-4.16How to use a DOI?

Abstract

The presentation of Lie (super)algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. It is very important, for instance, for investigation of the particular Lie (super)algebras arising in different (super)symmetric physical models. Generally, one can put the following question: what is the most general Lie algebra or superalgebra satisfying to the given set of Lie polynomial equations? To solve this problem, one has to perform a large volume of algebraic transformations which sharply increases with growth of the number of generators and relations. By this reason, in practice, one needs to use a computer algebra tool. We describe here an algorithm and its implementation in C for constructing the bases of finitely presented Lie (super)algebras and their commutator tables.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V.P. Gerdt
AU  - V.V. Kornyak
PY  - 1995
DA  - 1995/09/01
TI  - Lie Algebras and Superalgebras Defined by a Finite Number of Relations: Computer Analysis
JO  - Journal of Nonlinear Mathematical Physics
SP  - 367
EP  - 373
VL  - 2
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1995.2.3-4.16
DO  - 10.2991/jnmp.1995.2.3-4.16
ID  - Gerdt1995
ER  -