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On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups
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- Journal:
- Canadian Mathematical Bulletin / Volume 51 / Issue 2 / 01 June 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 261-282
- Print publication:
- 01 June 2008
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- Article
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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.
