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arXiv · 2604.00450

Point modules over the universal enveloping algebras of color Lie algebras

Shu Minaki
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Abstract

Let $k$ be an algebraically closed field with characteristic zero. In this paper, we define the notion of a $q'$-Heisenberg normal element of a $\mathbb{Z}$-graded $k$-algebra. This $q'$-Heisenberg normal element gives the structure of some sets of modules related to point modules. We also determine the set of point modules over an Artin--Schelter regular algebra obtained as the universal enveloping algebra of a color Lie algebra. Moreover, we give a concrete integer such that the inverse system of its truncated point schemes is constant. This is a quantitative answer to a question raised by Artin--Tate--Van den Bergh, in our setting.

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Shu Minaki. 2026-04-01. Point modules over the universal enveloping algebras of color Lie algebras. https://arxiv.org/abs/2604.00450

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