Solutions of associative Yang–Baxter equation and D−equation in low dimensions and associated Frobenius algebras and Connes cocycles

Abstract

In this work, we compute solutions of the Yang–Baxter associative equation in dimensions one and two. For these solutions, we describe the double constructions of the associated Frobenius algebras, following Bai’s definitions. Besides, we determine related compatible dendriform algebras and solutions of their [Formula: see text]equations. Finally, using symmetric solutions of these equations, we build the double constructions of related Connes cocycles.