Gröbner-Shirshov Bases and Hilbert Series of Free Dendriform Algebras
arXiv:1009.0185
Abstract
In this paper, we give a Gröbner-Shirshov basis of the free dendriform algebra as a quotient algebra of an -algebra. As applications, we obtain a normal form of the free dendriform algebra. Moreover, Hilbert series and Gelfand-Kirillov dimension of finitely generated free dendriform algebras are obtained.
arXiv comment12 pages
Cited by in corpus (4)
- Special identities for the pre-Jordan product in the free dendriform algebra
- Dendriform analogues of Lie and Jordan triple systems
- Gröbner-Shirshov bases for the non-symmetric operads of dendriform algebras and quadri-algebras (unabridged version)
- Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures