On the algebra of quasi-shuffles.

DOI10.1007/s00229-007-0086-2zbMath1126.16029arXivmath/0506498OpenAlexW2075993933MaRDI QIDQ884990

Jean-Louis Loday

Publication date: 7 June 2007

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506498

zbMATH Keywords

coalgebrasbialgebrasoperadsquasi-shuffle algebrastensor modulesshuffle productscommutative tri-dendriform algebras

Mathematics Subject Classification ID

Related Items (30)

On the Kantor product ⋮ Coherent unit actions on braided operads and Hopf algebras ⋮ Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras ⋮ Braided cofree Hopf algebras and quantum multi-brace algebras ⋮ A set-operad of formal fractions and dendriform-like sub-operads ⋮ From quantum quasi-shuffle algebras to braided Rota-Baxter algebras. ⋮ The algebraic and geometric classification of Zinbiel algebras ⋮ Braided Rota–Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras ⋮ Split Hopf algebras, quasi-shuffle algebras, and the cohomology of \(\Omega \Sigma X\) ⋮ Splitting of operads and Rota-Baxter operators on operads ⋮ Tridendriform structures ⋮ Functorial PBW theorems for post-Lie algebras ⋮ Zinbiel superalgebras ⋮ Generalized iterated-sums signatures ⋮ Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras. ⋮ Renormalization of multiple zeta values ⋮ Generating functions from the viewpoint of Rota-Baxter algebras ⋮ Cacti and filtered distributive laws ⋮ Poisson bialgebras ⋮ New directions in rough path theory. Abstracts from the workshop held December 6--12, 2020 (online meeting) ⋮ Lie Theory for Quasi-Shuffle Bialgebras ⋮ Natural endomorphisms of quasi-shuffle Hopf algebras ⋮ Quantum quasi-shuffle algebras. ⋮ From left modules to algebras over an operad: application to combinatorial Hopf algebras ⋮ Universal enveloping commutative Rota-Baxter algebras of pre- and post-commutative algebras ⋮ Quantum quasi-shuffle algebras. II. ⋮ Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras ⋮ Generalized Shuffles Related to Nijenhuis andTD-Algebras ⋮ Homotopy-theoretically enriched categories of noncommutative motives ⋮ Symmetric Zinbiel superalgebras

Cites Work

• Non-commutative Hopf algebra of formal diffeomorphisms.
• Homology of generalized partition posets
• Renormalization as a functor on bialgebras
• Integrable renormalization. II: The general case
• Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
• Baxter algebras and shuffle products
• Quasi-shuffle products
• On the structure of Hopf algebras
• Rational homotopy theory
• On the structure of free Baxter algebras
• On the structure of cofree Hopf algebras
• L'algebre de hopf bitensorielle
• Derivation and double shuffle relations for multiple zeta values
• Pre-Poisson algebras
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