English

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

Quantum Algebra 2012-10-30 v3

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.

Keywords

Cite

@article{arxiv.1107.6021,
  title  = {On embedding of dendriform algebras into Rota---Baxter algebras},
  author = {V. Yu. Gubarev and P. S. Kolesnikov},
  journal= {arXiv preprint arXiv:1107.6021},
  year   = {2012}
}

Comments

v3: a few new proofs added