2017/12/19 by Mahouton Norbert Hounkonnou, Hounkonnou, Mahouton Norbert, Gbêvèwou Damien Houndédji +2
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) #math.RA #msc:05C25 #msc:16S99 #msc:16T25 #msc:16Z05
paper · pdf · doi:10.48550/arxiv.1712.07152
arxiv created 2017/12/19 · openalex publication_date 2017/12/19 · arxiv updated 2017/12/21 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We consider the three-dimensional associative algebra H consisting of the 3x3 strictly upper triangular matrices whose the commutator is the Heisenberg Lie algebra. We determine the solutions of the Yang-Baxter associative equation in H. For the antisymmetric solutions, the corresponding bialgebraic structures, double constructions of Frobenius algebras and properties are given explicitly.Besides, we determine some related compatible dendriform algebras and solutions of their D-equations. Using symmetric solutions of these equations, we build the double constructions of related Connes cocycles. Finally, we compute solutions of the three-dimensional non decomposable associative Yang-Baxter equation and build the double constructions of associated Frobenius algebras.