Rota-Baxter algebras and new combinatorial identities

DOI10.1007/s11005-007-0168-9zbMath1121.05008arXivmath/0701031OpenAlexW1986036527MaRDI QIDQ2641438

José M. Gracia-Bondía, Kurusch Ebrahimi-Fard, Frédéric Patras

Publication date: 20 August 2007

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701031

zbMATH Keywords

Hopf algebraDynkin idempotentpre-Lie relationNoncommutative symmetric functionsRota-Baxter relationWord problemBogoliubov recursionBohnenblust-Spitzer identitiesFree algebrasQuasi-symmetric functions

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Associative rings and algebras arising under various constructions (16S99)

Related Items

Deformations of shuffles and quasi-shuffles, Rota-Baxter Leibniz algebras and their constructions, Exponential renormalization, Time-ordering and a generalized Magnus expansion, Logarithmic derivatives and generalized Dynkin operators, Weak quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras, Rota–Baxter operators on BiHom-associative algebras and related structures, The pre-Lie structure of the time-ordered exponential, Construction of Rota-Baxter algebras via Hopf module algebras., New identities in dendriform algebras, Weighted infinitesimal unitary bialgebras on free monoid algebras, Rota–Baxter Hom-Lie–Admissible Algebras, Quasi-idempotent Rota-Baxter operators arising from quasi-idempotent elements, Enumeration and generating functions of Rota-Baxter words., Dendriform equations, Operated semigroups, Motzkin paths and rooted trees, Rota-Baxter operators on pre-Lie superalgebras, Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras.

Cites Work

• Combinatorics of renormalization as matrix calculus
• On Dynkin and Klyachko idempotents in graded bialgebras
• An analytic problem whose solution follows from a simple algebraic identity
• A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion
• Trees, set compositions and the twisted descent algebra
• The descent algebra of a graded bialgebra
• Integrable renormalization. II: The general case
• Noncommutative symmetric functions
• Loday-type algebras and the Rota-Baxter relation
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion
• A Lie theoretic approach to renormalization
• On the structure of free Baxter algebras
• Some aspects of Baxter's functional equation
• From time-ordered products to Magnus expansion
• A Combinatorial Lemma and Its Application to Probability Theory
• HOPF ALGEBRAS IN DYNAMICAL SYSTEMS THEORY
• FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES
• Decomposition of time-ordered products and path-ordered exponentials
• Baxter algebras and combinatorial identities. I
• The Hopf algebra approach to Feynman diagram calculations
• Pre-Poisson algebras
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