Volume 2, Issue 3-4, September 1995, Pages 367 - 373
Lie Algebras and Superalgebras Defined by a Finite Number of Relations: Computer Analysis
- V.P. GERDT, V.V. KORNYAK
- Corresponding Author
- V.P. GERDT
Available Online 19 December 2006.
- https://doi.org/10.2991/jnmp.1995.2.3-4.16How to use a DOI?
- 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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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 -