Loday-Type Algebras and the Rota–Baxter Relation

By Kurusch Ebrahimi-Fard. 2002

225 citations recorded by the source corpus.

In this brief Letter, we would like to report on an observation concerning the relation between Rota–Baxter operators and Loday-type algebras, i.e. dendriform di- and tri-algebras. It is shown that associative algebras equipped with a Rota–Baxter operator of arbitrary weight always give such dendriform structures.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/45c809255c545dc0e1b11348c71ce8b24242e0e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Mixable shuffles, quasi-shuffles and Hopf algebras (2005, background): “In recent years, Rota-Baxter algebras have found applications in quantum field theory [8, 9, 15, 16, 17], dendriform algebras [1, 10, 13, 31], number theory [22], Hopf algebras [2] and combinatorics [21].”
FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES (2005, methodology): “In fact, such a relation for Lie algebras was introduced independently by Belavin and Drinfeld [8], and Semenov-Tian-Shansky [58] in the 1980s, under the disguise of r-matrices, of the (modified) classical Yang–Baxter equation, named after the physicists Chen-ning Yang and Rodney Baxter.”
Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras (2019, background): “For the classical case of one linear operator, see [2, 16] Theorem 3.”
Spitzer's identity and the algebraic Birkhoff decomposition in pQFT (2004, background): “On the mathematics side we would like to underline its intimate link to Loday’s dendriform algebra structures [1, 12, 14, 23, 24].”
On products and duality of binary, quadratic, regular operads (2004, background): “The first instance of such algebras, the dendriform dialgebra, has a string of two operators.”
Rota–Baxter algebras and dendriform algebras (2005, background): “[27] K. Ebrahimi-Fard, L. Guo and D. Kreimer, Spitzer’s Identity and the Algebraic Birkhoff Decomposition in pQFT, J. Phys.”
Rota–Baxter Hom-Lie–Admissible Algebras (2011, background): “Rota-Baxter algebras are related to dendriform algebras via a pair of adjoint functors [24, 26].”