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

Published online by Cambridge University Press:  20 November 2018

Karl-Hermann Neeb
Karl-Hermann Neeb*
Affiliation:
Technische Universität Darmstadt, Schlossgartenstrasse 7, D-64289 Darmstadt, Deutschland e-mail: neeb@mathematik.tu-darmstadt.de
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Abstract

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An $n$-dimensional quantum torus is a twisted group algebra of the group ${{\mathbb{Z}}^{n}}.$ 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

16S35quantum torusnormal formautomorphisms of quantum tori
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 2 , 01 June 2008 , pp. 261 - 282
Copyright
Copyright © Canadian Mathematical Society 2008

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