Embedding of dendriform algebras into Rota-Baxter algebras
By Vsevolod Gubarev, Pavel S. Kolesnikov. 2011
101 citations recorded by the source corpus.
Following a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (in press), DOI: 10.1093/imrn/rnr266] we define what is a dendriform dior trialgebra corresponding to an arbitrary variety Var of binary algebras (associative, commutative, Poisson, etc.). We call such algebras di- or tri-Var-dendriform algebras, respectively. We prove in general that the operad governing the variety of di- or tri-Var-dendriform algebras is Koszul dual to the operad governing di- or trialgebras corresponding to Var!. We also prove that every di-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of weight zero in the variety Var, and every tri-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of nonzero weight in Var.
Subfields: Algebra and Number Theory, Geometry and Topology, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/606b5af987a611587f812e388860123479311d23
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Citations in the corpus
- Rota—Baxter groups, skew left braces, and the Yang—Baxter equation (2021, result): “The proof and the ideology which is behind it come from the analogous result stated for Rota—Baxter algebras and so called postalgebras [17].”