Mahouton Norbert Hounkonnou

Center-symmetric Algebras and Bialgebras: Relevant Properties and Consequences

Lie admissible algebra structures, called center-symmetric algebras, are defined. Their main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of the underlying vector space and a finite-dimensional vector space. Then, the matched pair of center-symmetric algebras is established and related to the matched pair of sub-adjacent Lie algebras. Besides, Manin triples of center-symmetric algebras are defined and linked with their associated matched pairs. Further, center-symmetric bialgebras of center-symmetric algebras are investigated and discussed. Finally, a theorem yielding the equivalence between Manin triples of center-symmetric algebras, matched pairs of Lie algebras and center-symmetric bialgebras is provided.

Solutions of associative Yang-Baxter equation and

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-

D-

equation in low dimensions and associated Frobenius algebras and Connes cocycles

equations. Finally, using symmetric solutions of the latter equations, we proceed to double constructions of corresponding Connes cocycles.