2017/04/16 by Ni, Xiang, Bai, Chengming
#16W30 #17A30 #18D50 #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1704.04781
We introduce the notion of a quadri-bialgebra, which gives a bialgebra theory for the quadri-algebra introduced by Aguiar and Loday. We show that a quadri-bialgebra is equivalent to a Manin triple of dendriform algebras associated to a nondegenerate 2-cocycle, and to a Manin triple of quadri-algebras associated to a nondegenerate invariant bilinear form. Quadri-bialgebras also come from a variation of the classical Yang-Baxter equation, called the Q-equations. Moreover, quadri-bialgebras fit into the framework of construction of Rota-Baxter operators and Nijenhuis operators on the double spaces of quadri-algebras.