Groebner-Shirshov bases for dialgebras

Details Groebner-Shirshov bases for dialgebras Groebner-Shirshov bases for dialgebras

2008-04-04

arxiv.org/abs/0804.0638v4

International Journal of Algebra and Computation, 20(3)(2010), 391-415

Mathematics

Rings and Algebras

23 pages

Scientific paper

10.1142/S0218196710005753

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.

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