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.
| Comments: | 16 pages |
| Subjects: | Rings and Algebras (math.RA) |
| MSC classes: | 14A22 (Primary) 16S38, 17B35, 17B75 (Secondary) |
| Cite as: | arXiv:2604.00450 [math.RA] |
| (or arXiv:2604.00450v3 [math.RA] for this version) | |
| https://doi.org/10.48550/arXiv.2604.00450 arXiv-issued DOI via DataCite |
From: Shu Minaki [view email]
[v1]
Wed, 1 Apr 2026 03:58:42 UTC (18 KB)
[v2]
Sat, 11 Apr 2026 15:27:06 UTC (21 KB)
[v3]
Tue, 26 May 2026 10:07:47 UTC (21 KB)
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