Double constructions of Heisenberg Frobenius algebras and Connes\n cocycles, and solutions of the three-dimensional associative Yang-Baxter\n equation

2017/12/19 by Mahouton Norbert Hounkonnou, Hounkonnou, Mahouton Norbert, Gbêvèwou Damien Houndédji +1
Mathematics · Physics and Astronomy · #05C25 #16S99 #16T25 #16Z05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1712.07152

openalex publication_date 2017/12/19 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider the three-dimensional associative algebra H consisting of the 3x3\nstrictly upper triangular matrices whose the commutator is the Heisenberg Lie\nalgebra. We determine the solutions of the Yang-Baxter associative equation in\nH. For the antisymmetric solutions, the corresponding bialgebraic structures,\ndouble constructions of Frobenius algebras and properties are given\nexplicitly.Besides, we determine some related compatible dendriform algebras\nand solutions of their D-equations. Using symmetric solutions of these\nequations, we build the double constructions of related Connes cocycles.\nFinally, we compute solutions of the three-dimensional non decomposable\nassociative Yang-Baxter equation and build the double constructions of\nassociated Frobenius algebras.\n

Citations

• On the Associative Analog of Lie Bialgebras
• Pairs of Compatible Associative Algebras, Classical Yang-Baxter Equation and Quiver Representations

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