Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Automorphisms of Quantum Polynomials (2102.02859v1)

Published 4 Feb 2021 in math.RA

Abstract: 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 $\wedge2 : \mathrm{GL}(n, \mathbb Z) \rightarrow \mathrm{GL}(\binom{n}{2}, \mathbb Z)$ of $\mathrm{GL}(n, \mathbb Z)$ and thus compute the non-scalar automorphism group $\mathrm{Aut}(\mathbb Zn, \lambda)$ 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 $\binom{n - 1}{2} + 1$ 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 ${(\mathbb F\ast)}n$.

Summary

We haven't generated a summary for this paper yet.