Universal Algebra Applied to Hom-Associative Algebras, and More
Rings and Algebras
2014-04-10 v1
Abstract
The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we review the main results. We discuss the envelopment problem, operads, and the Diamond Lemma; the usual tools have to be adapted to this new situation. Moreover we study Hilbert series for the hom-associative operad and free algebra, and describe them up to total degree equal 8 and 9 respectively.
Keywords
Cite
@article{arxiv.1404.2516,
title = {Universal Algebra Applied to Hom-Associative Algebras, and More},
author = {Lars Hellström and Abdenacer Makhlouf and Sergei D. Silvestrov},
journal= {arXiv preprint arXiv:1404.2516},
year = {2014}
}
Comments
Algebra, Geometry and Mathematical Physics, Mulhouse, France, October 2011