Beck modules and alternative algebras
Rings and Algebras
2024-12-24 v4
Abstract
We set out the general theory of ``Beck modules'' in a variety of algebras and describe them as modules over suitable ``universal enveloping'' unital associative algebras. We develop a theory of ``noncommutative partial differentiation'' to pass from the equations of the variety to relations in a universal enveloping algebra. We pay particular attention to the case of alternative algebras, defined by a restricted associative law, and determine the Poincar\'e polynomial of the universal enveloping algebra in the homogeneous case.
Cite
@article{arxiv.2309.07962,
title = {Beck modules and alternative algebras},
author = {Nishant Dhankhar and Haynes Miller and Ali Tahboub and Victor Yin},
journal= {arXiv preprint arXiv:2309.07962},
year = {2024}
}
Comments
21 pages. Version accepted by Communications in Algebra, with improvements following referee report