Groebner-Shirshov bases for dialgebras
arXiv:0804.0638 · doi:10.1142/S0218196710005753
Abstract
In this paper, we define the Gröbner-Shirshov basis for a dialgebra. The Composition-Diamond lemma for dialgebras is given then. As results, we give Gröbner-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.
23 pages