Rota-Baxter algebras and new combinatorial identities
arXiv:math/0701031 · doi:10.1007/s11005-007-0168-9
Abstract
The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are indicated.
8 pages, improved version
References in corpus (8)
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- A Lie theoretic approach to renormalization
- A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion
- Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
- Polynomial realizations of some trialgebras
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- Hopf algebras in dynamical systems theory
Cited by in corpus (20)
- A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion
- New identities in dendriform algebras
- Exponential renormalization
- Dendriform Equations
- Weak composition quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras
- Time-ordering and a generalized Magnus expansion
- The pre-Lie structure of the time-ordered exponential
- From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras
- Construction of Rota-Baxter algebras via Hopf module algebras
- Rota-Baxter Coalgebras
- The combinatorics of Bogoliubov's recursion in renormalization
- Rota-Baxter operators on BiHom-associative algebras and related structures
- The combinatorics of Green's functions in planar field theories
- Bialgebra structures of 2-associative algebras
- Rota-Baxter Operators on pre-Lie superalgebras and beyond
- Quasi-idempotent Rota-Baxter operators arising from quasi-idempotent elements
- Gröbner-Shirshov bases for Rota-Baxter algebras
- A Zassenhaus-type algorithm solves the Bogoliubov recursion
- Groebner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras
- Rota-Baxter Hom-Lie-admissible algebras