Abstract view
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On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups
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Published:2008-06-01
Printed: Jun 2008
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.
