Jacobi-Jordan (Conformal) algebras: Basics, Constructions, Cohomology and Deformations

Abstract: The aim of this talk is to provide an overview of recent developments on Jacobi-Jordan algebras and Jacobi-Jordan conformal algebras. We provide for Jacobi-Jordan algebras some basic constructions and define a cohomology based on two operators, called zigzag cohomology. We describe the relationships between first and second cohomology groups with extensions and deformations. Moreover, we consider cohomology properties of pseudo-euclidean Jacobi-Jordan algebras and provide a deformation theory that fits with our zigzag cohomology of Jacobi-Jordan algebras. Furtheremore, we introduce Jacobi-Jordan Conformal algebras and consider some related structures such as conformal modules, corresponding representations and O-operators. The talk is based on joint works with A. Baklouti , S. Benayadi, S. Mansour, T. Chtioui and S. Mabrouk.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar