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# On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups

Published:2008-06-01
Printed: Jun 2008
• Karl-Hermann Neeb
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## Abstract

An $n$-dimensional quantum torus is a twisted group algebra of the group $\Z^n$. It is called rational if all invertible commutators are roots of unity. In the present note we describe a normal form for rational $n$-dimensional quantum tori over any field. Moreover, we show that for $n = 2$ the natural exact sequence describing the automorphism group of the quantum torus splits over any field.
 Keywords: quantum torus, normal form, automorphisms of quantum tori
 MSC Classifications: 16S35 - Twisted and skew group rings, crossed products