Leonid A. Bokut, Yuqun Chen, “Gröbner–Shirshov bases and PBW theorems”, J. Sib. Fed. Univ. Math. Phys., 6:4 (2013), 417

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J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 4, Pages 417–427 (Mi jsfu327)

This article is cited in 5 scientific papers (total in 5 papers)

Gröbner–Shirshov bases and PBW theorems

Leonid A. Bokut^ab, Yuqun Chen^b

^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.

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UDC: 512.5
Received: 18.09.2013
Received in revised form: 02.10.2013
Accepted: 04.11.2013
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Citation: Leonid A. Bokut, Yuqun Chen, “Gröbner–Shirshov bases and PBW theorems”, J. Sib. Fed. Univ. Math. Phys., 6:4 (2013), 417–427

Citation in format AMSBIB

\Bibitem{BokChe13}

\by Leonid~A.~Bokut, Yuqun~Chen

\paper Gr\"obner--Shirshov bases and PBW theorems

\jour J. Sib. Fed. Univ. Math. Phys.

\yr 2013

\vol 6

\issue 4

\pages 417--427

\mathnet{http://mi.mathnet.ru/jsfu327}

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This publication is cited in the following articles:

Yu. Li, Q. Mo, “On free pre-Lie algebras”, Algebr. Colloq., 24:2 (2017), 267–284
P. Kolesnikov, “Gröbner-Shirshov bases for pre-associative algebras”, Commun. Algebr., 45:12 (2017), 5283–5296
Y. Li, Q. H. Mo, “Some new results for Leibniz algebras and non-associative algebras”, Southeast Asian Bull. Math., 41:1 (2017), 45–54
I. Ivanov-Pogodaev, S. Malev, “Finite Gröbner basis algebras with unsolvable nilpotency problem and zero divisors problem”, J. Algebra, 508 (2018), 575–588
Kanel-Belov A., Chilikov A., Ivanov-Pogodaev I., Malev S., Plotkin E., Yu J.-T., Zhang W., “Nonstandard Analysis, Deformation Quantization and Some Logical Aspects of (Non)Commutative Algebraic Geometry”, Mathematics, 8:10 (2020), 1694

Журнал Сибирского федерального университета. Серия "Математика и физика"

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