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

2015/09/03 by Hounkonnou, Mahouton Norbert, Houndedji, Gbevewou Damien
#05C25 #16S99 #16Z05 #2010: 16T25 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/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 D- equations. Finally, using symmetric solutions of the latter equations, we proceed to double constructions of corresponding Connes cocycles.

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