Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras

2008/07/14 by Li Guo, Guo, Li, Bingyong Xie +1
Mathematics · #05E99 #16W99 #18F20 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0807.2267

openalex publication_date 2008/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the ring theoretical structures of mixable shuffle algebras and their associated free commutative Rota-Baxter algebras. For this study we utilize the connection of the mixable shuffle algebras with the overlapping shuffle algebra of Hazewinkel, quasi-shuffle algebras of Hoffman and quasi-symmetric functions. This connection allows us to apply methods and results on shuffle products and Lyndon words on ordered sets. As a result, we obtain structure theorems for a large class of mixable shuffle algebras and free commutative Rota-Baxter algebras with various coefficient rings.

Citations

• On the Associative Analog of Lie Bialgebras

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