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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 272, Pages 26–67
(Mi znsl1362)
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This article is cited in 42 scientific papers (total in 42 papers)
Gróbner–Shirshov bases: from incipiency to nowdays
L. A. Bokut', P. S. Kolesnikov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
In this paper we present a history and the main results of the Gróbner–Shirshov bases theory for commutative, non-commutative, Lie and conformal algebras from the beginning (1962) up to nowadays. We consider the problem of constructing free Lie algebra basis, structure of free products of Lie algebras, word problem for Lie algebras, embedding of arbitrary Lie algebra into algebraically closed one. The contemporary form of Composition–Diamond lemma (CD-lemma) is adduced. The rewriting systems for groups are considered from the Gróbner–Shirshov bases theory point of view. The important role is devoted to conformal algebras, we present a statement of CD-lemma for associative conformal algebras, some examples are
considered. The analogue of Hilbert basis theorem for commutative conformal algebras is stated.
Received: 22.02.2000
Citation:
L. A. Bokut', P. S. Kolesnikov, “Gróbner–Shirshov bases: from incipiency to nowdays”, Problems in the theory of representations of algebras and groups. Part 7, Zap. Nauchn. Sem. POMI, 272, POMI, St. Petersburg, 2000, 26–67; J. Math. Sci. (N. Y.), 116:1 (2003), 2894–2916
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https://www.mathnet.ru/eng/znsl1362 https://www.mathnet.ru/eng/znsl/v272/p26
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