English

Groebner-Shirshov bases for dialgebras

Rings and Algebras 2010-09-03 v4

Abstract

In this paper, we define the Gr\"obner-Shirshov basis for a dialgebra. The Composition-Diamond lemma for dialgebras is given then. As results, we give Gr\"obner-Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension of a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above.

Keywords

Cite

@article{arxiv.0804.0638,
  title  = {Groebner-Shirshov bases for dialgebras},
  author = {L. A. Bokut and Yuqun Chen and Cihua Liu},
  journal= {arXiv preprint arXiv:0804.0638},
  year   = {2010}
}

Comments

23 pages

R2 v1 2026-06-21T10:27:34.446Z