Geodesic
Gelfand--Kirillov dimensions of simple modules over twisted group algebras $k \ast A$
Izvestiya. Mathematics , Tome 86 (2022) no. 4, pp. 715-726.

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For the $n$-dimensional multi-parameter quantum torus algebra $\Lambda_{\mathfrak q}$ over a field $k$ defined by a multiplicatively antisymmetric matrix $\mathfrak q = (q_{ij})$ we show that, in the case when the 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 simple modules. 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 without assuming the simplicity, and it is shown that a dichotomy still holds for the GK dimension of simple modules.
Keywords: Gelfand–Kirillov dimension, quantum torus, twisted group algebra
Mots-clés : simple module, Krull dimension. 
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Ashish Gupta; Umamaheswaran Arunachalam. Gelfand--Kirillov dimensions of simple modules over twisted group algebras $k \ast A$. Izvestiya. Mathematics , Tome 86 (2022) no. 4, pp. 715-726. http://geodesic.mathdoc.fr/item/IM2_2022_86_4_a3/

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