Gr\"obner-Shirshov Bases and Hilbert Series of Free Dendriform Algebras
Abstract
In this paper, we give a Gr\"obner-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.
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