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JOURNALS // Journal of Siberian Federal University. Mathematics & Physics // Archive
J. Sib. Fed. Univ. Math. Phys., 2013 Volume 6, Issue 4, Pages 417–427 (Mi jsfu327)
This article is cited in 6 papers

Gröbner–Shirshov bases and PBW theorems

Leonid A. Bokutab, Yuqun Chenb

a Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
b School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, P. R. China

Abstract: We review some applications of Gröbner–Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.

Keywords: Gröbner–Shirshov basis, Composition-Diamond lemma, PBW theorem, normal form, group, semigroup, extension.

UDC: 512.5

Received: 18.09.2013
Received in revised form: 02.10.2013
Accepted: 04.11.2013

Language: English


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