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

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

2005-11-10

arxiv.org/abs/math/0511263v5

Mathematics

Rings and Algebras

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

Scientific paper

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.

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