Groebner-Shirshov Bases for Algebras A_n⁽¹⁾, B_n⁽¹⁾
by
Evgeniy Poroshenko
Mechanical and Mathematikal Department Novosibirsk State University

The idea of Groebner-Shirshov basis was introduced by Shirshov in A.I.Shirshov, Some Algorithmic Problems for Lie Algebras, Siberian Math. J, 3 (1962), 292-296. There is number of properties of Groebner-Shirshov bases, which essentially simplify study of Lie algebras. There is the classical algorithm (Buchberger-Shirshov one) for constructing of Groebner-Shirshov bases but it is very laborious because it is necessary to compute a great number of compositions.

In this work we suggest an algorithm for search of Groebner-hirshov bases for Kac-Moody Lie algebras of the type X_n⁽¹⁾ where X=A,  B, ...,  G which is differ from Buchberger-Shirshov one. This algorithm uses the isomorphism of X_n⁽¹⁾ into the corresponding loop algebra. After that Groebner-Shirshov bases for Kac-Moody algebras of the types A_n⁽¹⁾, _n^(1)

Date received: June 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafe-12.