2021/02/04 by Ashish Gupta, Gupta, Ashish
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2102.02859
openalex publication_date 2021/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An important step in the determination of the automorphism group of the quantum torus of rank n (or twisted group algebra of \mathbb Zn) is the determination of its so-called non-scalar automorphisms. We present a new algorithimic approach towards this problem based on the bivector representation \wedge2 : GL(n, \mathbb Z) → GL(\binomn2, \mathbb Z) of GL(n, \mathbb Z) and thus compute the non-scalar automorphism group Aut(\mathbb Zn, λ) in several new cases. As an application of our ideas we show that the quantum polynomial algebra (multiparameter quantum affine space of rank n) has only scalar (or toric) automorphisms provided that the torsion-free rank of the subgroup generated by the defining multiparameters is no less than \binomn - 12 + 1 thus improving an earlier result. We also investigate the question: when is a multiparameter quantum affine space free of so-called linear automorphisms other than those arising from the action of the n-torus (\mathbb F^∗)n.