Log-ozone groups and centers of polynomial Poisson algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918087625801728 |
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| author | Chan, Kenneth Gaddis, Jason Won, Robert Zhang, James J. |
| author_facet | Chan, Kenneth Gaddis, Jason Won, Robert Zhang, James J. |
| contents | In previous work, the authors introduced the ozone group of an associative algebra as the subgroup of automorphisms which fix the center pointwise. The authors studied PI skew polynomial algebras, using the ozone group to understand their centers and to characterize them among graded algebras.
In this work, we introduce and study the log-ozone group of a Poisson algebra over a field of positive characteristic. The log-ozone group is then used to characterize polynomial Poisson algebras with skew symmetric structure. We prove that unimodular Poisson algebras with skew symmetric structure have Gorenstein centers. A related result is proved for graded polynomial Poisson algebras of dimension three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Log-ozone groups and centers of polynomial Poisson algebras Chan, Kenneth Gaddis, Jason Won, Robert Zhang, James J. Rings and Algebras 17B63, 17B40, 16W25, 16S36 In previous work, the authors introduced the ozone group of an associative algebra as the subgroup of automorphisms which fix the center pointwise. The authors studied PI skew polynomial algebras, using the ozone group to understand their centers and to characterize them among graded algebras. In this work, we introduce and study the log-ozone group of a Poisson algebra over a field of positive characteristic. The log-ozone group is then used to characterize polynomial Poisson algebras with skew symmetric structure. We prove that unimodular Poisson algebras with skew symmetric structure have Gorenstein centers. A related result is proved for graded polynomial Poisson algebras of dimension three. |
| title | Log-ozone groups and centers of polynomial Poisson algebras |
| topic | Rings and Algebras 17B63, 17B40, 16W25, 16S36 |
| url | https://arxiv.org/abs/2507.06940 |