Jacobi-Jordan conformal algebras: Basics, Constructions and related structures
Abstract
The main purpose of this paper is to introduce and investigate the notion of Jacobi-Jordan conformal algebra. They are a generalization of Jacobi-Jordan algebras which correspond to the case in which the formal parameter lambda equals 0. We consider some related structures such as conformal modules, corresponding representations and O-operators. Therefore, conformal derivations from Jacobi-Jordan conformal algebras to their conformal modules are used to describe conformal derivations of Jacobi-Jordan conformal algebras of semidirect product type. Moreover, we study a class of Jacobi-Jordan conformal algebras called quadratic Jacobi-Jordan conformal algebras, which are characterized by mock-Gel'fand Dorfman bialgebras. Finally, the C[delta]-split extending structures problem for Jacobi-Jordan conformal algebras is studied. Furthermore, we introduce an unified product of a given Jacobi-Jordan conformal algebra and a given C[delta]-module K. This product includes some other interesting products of Jacobi-Jordan conformal algebras such as twisted product or crossed product. Using this product, a cohomological type object is constructed to provide a theoretical answer to the C[delta]-split extending structures problem.
Cite
@article{arxiv.2401.02206,
title = {Jacobi-Jordan conformal algebras: Basics, Constructions and related structures},
author = {Taoufik Chtioui and Sami Mabrouk and Abdenacer Makhlouf},
journal= {arXiv preprint arXiv:2401.02206},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2202.08575 by other authors