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.
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