Point modules over the universal enveloping algebras of color Lie algebras

TL;DR

This paper characterizes point modules over universal enveloping algebras of color Lie algebras, introducing a new notion of $q'$-Heisenberg normal elements to analyze module structures.

Contribution

It defines $q'$-Heisenberg normal elements and determines point modules over universal enveloping algebras of color Lie algebras, providing explicit descriptions.

Findings

Set of point modules over certain Artin--Schelter regular algebras is determined.

Introduces $q'$-Heisenberg normal elements to study module structures.

Identifies a concrete integer for the stability of truncated point schemes.

Abstract

Let $k$ be an algebraically closed field with characteristic $0$. 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. Also, we 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 truncated point schemes of it is constant.