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

http://dx.doi.org/10.4153/CMB-2008-027-7
Canad. Math. Bull. 51(2008), 261-282

  Published:2008-06-01
 Printed: Jun 2008

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.