Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras-Reference-Cited by-同舟云学术

Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras

Published:2017-01 Issue:01 Volume:16 Page:1750001
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Bokut L. A.¹²³,Chen Yuqun¹,Zhang Zerui¹

Affiliation:

1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China

2. Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, Novosibirsk, Russian Federation

3. Department of Mathematics and Mechanics, Novosibirsk State University, ul. Pirogova 2, Novosibirsk, Russian Federation

Abstract

We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817500013

Reference42 articles.

1. The classification of Novikov algebras in low dimensions

2. The classification of Novikov algebras in low dimensions: invariant bilinear forms

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