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

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

2011-07-29

arxiv.org/abs/1107.6021v3

Mathematics

Quantum Algebra

v3: a few new proofs added

Scientific paper

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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