Solutions of associative Yang-Baxter equation and equation in low dimensions and associated Frobenius algebras and Connes cocycles
arXiv:1509.01129
Abstract
This work addresses some relevant characteristics of associative algebras in low dimensions. Especially, given 1 and 2 dimensional associative algebras, we explicitly solve associative Yang-Baxter equations and use skew-symmetric solutions to perform double constructions of Frobenius algebras. Besides, we determine related compatible dendriform algebras and solutions of their equations. Finally, using symmetric solutions of the latter equations, we proceed to double constructions of corresponding Connes cocycles.
arXiv commentarXiv admin note: text overlap with arXiv:0808.3330 by other authors