Mixable shuffles, quasi-shuffles and Hopf algebras.

DOI10.1007/s10801-006-9103-xzbMath1103.16025arXivmath/0506418OpenAlexW1971645711MaRDI QIDQ2498443

Li Guo, Kurusch Ebrahimi-Fard

Publication date: 16 August 2006

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506418

zbMATH Keywords

Hopf algebrasfree Rota-Baxter algebrasshuffle productsquasi-shuffle products

Mathematics Subject Classification ID

Related Items (46)

Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras ⋮ Braided cofree Hopf algebras and quantum multi-brace algebras ⋮ From quantum quasi-shuffle algebras to braided Rota-Baxter algebras. ⋮ Flows and stochastic Taylor series in Itô calculus ⋮ Free Rota-Baxter systems and a Hopf algebra structure ⋮ Braided Rota–Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras ⋮ Weak stuffle algebras ⋮ Localization of Rota-Baxter algebras ⋮ Rota-Baxter paired modules and their constructions from Hopf algebras ⋮ Embedding of dendriform algebras into Rota-Baxter algebras ⋮ HOPF ALGEBRAS IN DYNAMICAL SYSTEMS THEORY ⋮ Modules of non-unital polynomial Rota-Baxter algebras ⋮ Polylogarithms and multiple zeta values from free Rota-Baxter algebras ⋮ Rota-Baxter algebras and left weak composition quasi-symmetric functions ⋮ Representations of the Laurent series Rota-Baxter algebras and regular-singular decompositions ⋮ λ-TD algebras, generalized shuffle products and left counital Hopf algebras ⋮ FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES ⋮ Weak quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras ⋮ The algebra of Hurwitz multizeta functions ⋮ Renormalization of multiple zeta values ⋮ Rota-Baxter algebras and dendriform algebras. ⋮ Generating functions from the viewpoint of Rota-Baxter algebras ⋮ Free integro-differential algebras and Gröbner-Shirshov bases. ⋮ On differential Rota-Baxter algebras. ⋮ Constructions of Free Commutative Integro-Differential Algebras ⋮ Free Lie Rota-Baxter algebras ⋮ Counterterms in the context of the universal Hopf algebra of renormalization ⋮ Rota-Baxter operators on 4-dimensional complex simple associative algebras ⋮ Natural endomorphisms of quasi-shuffle Hopf algebras ⋮ Quantum quasi-shuffle algebras. ⋮ CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES ⋮ On products and duality of binary, quadratic, regular operads ⋮ FROM DYSON–SCHWINGER EQUATIONS TO THE RIEMANN–HILBERT CORRESPONDENCE ⋮ Universal enveloping commutative Rota-Baxter algebras of pre- and post-commutative algebras ⋮ Hopf Algebras in Renormalisation ⋮ On weak peak quasisymmetric functions ⋮ Quantum quasi-shuffle algebras. II. ⋮ Universal enveloping associative Rota-Baxter algebras of preassociative and postassociative algebra ⋮ Lévy processes and quasi-shuffle algebras ⋮ On Hurwitz multizeta functions ⋮ Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Free modified Rota-Baxter algebras and Hopf algebras ⋮ Differential algebraic Birkhoff decomposition and the renormalization of multiple zeta values ⋮ Generalized Shuffles Related to Nijenhuis andTD-Algebras ⋮ Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras ⋮ Structure Theorems of Mixable Shuffle Algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ennea-algebras
• Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula
• An analytic problem whose solution follows from a simple algebraic identity
• On the Hopf algebra strucutre of perturbative quantum field theories
• Representations of Hopf algebras arising from Lie algebras of Cartan type
• The algebra of multiple harmonic series
• The algebra and combinatorics of shuffles and multiple zeta values
• Multiple \(q\)-zeta values
• Integrable renormalization. II: The general case
• Loday-type algebras and the Rota-Baxter relation
• Relations of multiple zeta values and their algebraic expression.
• On the associative Nijenhuis relation
• Quadri-algebras
• Baxter algebras and shuffle products
• Quasi-shuffle products
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• On free Baxter algebras: Completions and the internal construction
• Ten mathematics problems I will never solve
• Rota-Baxter algebras and dendriform algebras.
• On products and duality of binary, quadratic, regular operads
• On the structure of free Baxter algebras
• A Combinatorial Lemma and Its Application to Probability Theory
• Baxter algebras and combinatorial identities. II
• Baxter algebras and Hopf algebras
• Spitzer's identity and the algebraic Birkhoff decomposition in pQFT
• Integrable renormalization I: The ladder case
• BAXTER ALGEBRAS, STIRLING NUMBERS AND PARTITIONS
• Baxter algebras and combinatorial identities. I
• Chen's iterated integral represents the operator product expansion
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.
• Baxter algebras and the umbral calculus

This page was built for publication: Mixable shuffles, quasi-shuffles and Hopf algebras.