Point modules over the universal enveloping algebras of color Lie algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917535657492480 |
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| author | Minaki, Shu |
| author_facet | Minaki, Shu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00450 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Point modules over the universal enveloping algebras of color Lie algebras Minaki, Shu Rings and Algebras 14A22 (Primary) 16S38, 17B35, 17B75 (Secondary) 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. |
| title | Point modules over the universal enveloping algebras of color Lie algebras |
| topic | Rings and Algebras 14A22 (Primary) 16S38, 17B35, 17B75 (Secondary) |
| url | https://arxiv.org/abs/2604.00450 |