Deforming algebras with anti-involution via twisted associativity
Rings and Algebras
2023-10-03 v1
Abstract
This contribution studies a specific deformation of algebras with anti-involution. Starting with the observation that twisting the multiplication of such an algebra by its anti-involution generates a Hom-associative algebra of type II, it formulates the adequate modules theory over these algebras, and shows that there is a faithful functor from the category of finite-dimensional left modules of algebras with involution to finite-dimensional right modules of Hom-associative algebras of type II. It ends with a discussion on a diagrammatic operadic approach to generalize the study of such deformations.
Cite
@article{arxiv.2106.01855,
title = {Deforming algebras with anti-involution via twisted associativity},
author = {Alexis Langlois-Rémillard},
journal= {arXiv preprint arXiv:2106.01855},
year = {2023}
}
Comments
21p. some TikZ figures, submitted as a contribution to the proceedings of SPAS 2019, V\"aster\r{a}s