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 $L$-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.
12 pages