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arXiv · 2309.07962

Beck modules and alternative algebras

Nishant Dhankhar·Haynes Miller·Ali Tahboub·Victor Yin
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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.

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Nishant Dhankhar, Haynes Miller, Ali Tahboub, Victor Yin. 2023-09-14. Beck modules and alternative algebras. https://arxiv.org/abs/2309.07962

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