NEW IDENTITIES IN DENDRIFORM ALGEBRAS
By Kurusch Ebrahimi-Fard, Dominique Manchon, Frédéric Patras. 2007
60 citations recorded by the source corpus.
Abstract Dendriform structures arise naturally in algebraic combinatorics (where they allow, for example, the splitting of the shuffle product into two pieces) and through Rota–Baxter algebra structures (the latter appear, among others, in differential systems and in the renormalization process of pQFT). We prove new combinatorial identities in dendriform algebras that appear to be strongly related to classical phenomena, such as the combinatorics of Lyndon words, rewriting rules in Lie algebras, or the fine structure of the Malvenuto–Reutenauer algebra. One of these identities is an abstract noncommutative, dendriform, generalization of the Bohnenblust–Spitzer identity and of an identity involving iterated Chen integrals due to C.S. Lam.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/851c8bd8d9d6e8cabee09c9bb7738f207c2dfe7f
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In Algebra and Number Theory
- Abdenacer Makhlouf
- Donald Yau
- Sergei Silvestrov
- F. Ammar
- Aron Gohr
- Florin Panaite
- Y. Sheng
- S. Benayadi
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Abdenacer Makhlouf
- Donald Yau
- F. Ammar
- Florin Panaite
- Sergei Silvestrov
- Aron Gohr
- Y. Sheng
- S. Benayadi
Citations in the corpus
- Rota–Baxter Hom-Lie–Admissible Algebras (2011, methodology): “ity appeared under the name multiplicativity constraint. This seminal work givesrise to an important development including Rota-Baxter algebras and their connections to other algebraic structure. See [2, 4, 24, 25, 27, 28, 29, 30, 31, 32, 33, 38, 39, 40, 41, 42, 51, 10]. Rota-Baxter operator in the ”