1. CMB 2008 (vol 51 pp. 261)
|On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups |
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.
Keywords:quantum torus, normal form, automorphisms of quantum tori