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arXiv · 0909.3601

Colored trees and noncommutative symmetric functions

Matthew Szczesny
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Abstract

Let $\CRF_S$ denote the category of $S$-colored rooted forests, and $\H_{\CRF_S}$ denote its Ringel-Hall algebra as introduced in \cite{KS}. We construct a homomorphism from a $K^+_0 (\CRF_S)$--graded version of the Hopf algebra of noncommutative symmetric functions to $\H_{\CRF_S}$. Dualizing, we obtain a homomorphism from the Connes-Kreimer Hopf algebra to a $K^+_0 (\CRF_S)$--graded version of the algebra of quasisymmetric functions. This homomorphism is a refinement of one considered by W. Zhao in \cite{Z}.

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Matthew Szczesny. 2009-09-19. Colored trees and noncommutative symmetric functions. https://arxiv.org/abs/0909.3601

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