2018/12/06 by Ashish Gupta, Gupta, Ashish, Umamaheswaran Arunachalam +1
Mathematics · Physics and Astronomy · #16D60 #16P90 #16S35 #16S80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1812.02629
openalex publication_date 2018/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the n-dimensional multiparameter quantum torus algebra Λ\mathfrak q over a field k defined by a multiplicatively antisymmetric matrix \mathfrak q = (qij) we show that in the case when the torsion-free rank of the subgroup of k^× generated by the qij is large enough there is a characteristic set of values (possibly with gaps) from 0 to n that can occur as the Gelfand--Kirillov dimension of simple modules. The special case when K.dim(Λ\mathfrak q) = n - 1 and Λ\mathfrak q is simple studied in A.~Gupta, \it \uppercaseGK-dimensions of simple modules over K[X± 1, σ], Comm. Algebra, \bf 41(7) (2013), 2593--2597 is considered without assuming simplicity and it is shown that a dichotomy still holds for the GK dimension of simple modules.