On the classification of rational quantum tori and the structure of their automorphism group

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.

Section II has been reformulated, in part. Prop. II.3. Due to a hint of Ph. Gille, Problem II is now taken care of