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arXiv · 1107.6021

On embedding of dendriform algebras into Rota---Baxter algebras

V. Yu. Gubarev·P. S. Kolesnikov
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Abstract

Following a recent work by C. Bai, O. Bellier, L. Guo, and X. Ni (arXiv:1106.6080) we define what is a dendriform di- or trialgebra in an arbitrary variety Var of algebras (associative, commutative, Poisson, etc.). We prove that every dendriform dialgebra in Var can be embedded into a Rota---Baxter algebra of weight zero in the same variety, and every dendriform trialgebra can be embedded into a Rota---Baxter algebra of nonzero weight.

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V. Yu. Gubarev, P. S. Kolesnikov. 2011-07-29. On embedding of dendriform algebras into Rota---Baxter algebras. https://doi.org/10.2478/s11533-012-0138-z

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