Embedding of dendriform algebras into Rota-Baxter algebras

作者：Gubarev Vsevolod Yu^*; Kolesnikov Pavel S

来源：Central European Journal of Mathematics, 2013, 11(2): 226-245.

DOI：10.2478/s11533-012-0138-z

• Dendriform algebra
• Dialgebra
• Trialgebra
• Rota-Baxter operator
• Operad
• Manin product
• Conformal algebra

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 di- or 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(1). 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.

• 出版日期2013-2