Gelfand–Kirillov dimensions of simple modules over twisted group algebras $k \ast A$
- Autores: Gupta A.1, Arunachalam U.2
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Afiliações:
- Ramakrishna Mission Vivekananda Educational and Research Institute
- Harish-Chandra Research Institute
- Edição: Volume 86, Nº 4 (2022)
- Páginas: 103-115
- Seção: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/133877
- DOI: https://doi.org/10.4213/im9182
- ID: 133877
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Resumo
For the $n$-dimensional multi-parameter quantum torus algebra $\Lambda_{\mathfrak q}$ over a field $k$ defined by a multiplicativelyantisymmetric matrix $\mathfrak q = (q_{ij})$ we show that, in the case whenthe torsion-free rank of the subgroup of $k^\times$ generated by the $q_{ij}$is large enough, there is a characteristic set of values (possibly with gaps)from $0$ to $n$ that can occur as the Gelfand–Kirillov dimensions of simplemodules. The special case when $\mathrm{K}.\dim(\Lambda_{\mathfrak q}) = n - 1$and $\Lambda_{\mathfrak q}$ is simple, studied in A. Gupta, $\mathrm{GK}$-dimensions of simple modules over $K[X^{\pm 1},\sigma]$, Comm. Algebra, 41(7) (2013), 2593–2597, is considered withoutassuming the simplicity, and it is shown that a dichotomy still holds for theGK dimension of simple modules.
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Sobre autores
Ashish Gupta
Ramakrishna Mission Vivekananda Educational and Research Institute
Email: a0gupt@gmail.com
Umamaheswaran Arunachalam
Harish-Chandra Research Institute
Email: ruthreswaran@gmail.com
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