Journal of Nonlinear Mathematical Physics

Volume 2, Issue 3-4, September 1995, Pages 367 - 373

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

Authors
V.P. GERDT, V.V. KORNYAK
Corresponding Author
V.P. GERDT
Available Online 19 December 2006.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
2 - 3
Pages
367 - 373
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1995.2.3-4.16How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - V.P. GERDT
AU  - V.V. KORNYAK
PY  - 2006
DA  - 2006/12
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  - https://doi.org/10.2991/jnmp.1995.2.3-4.16
ID  - GERDT2006
ER  -