English

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

Rings and Algebras 2007-05-23 v5 Group Theory

Abstract

An n-dimensional quantum torus is a twisted group algebra of the group Zn\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=2n = 2 the natural exact sequence describing the automorphism group of the quantum torus splits over any field.

Keywords

Cite

@article{arxiv.math/0511263,
  title  = {On the classification of rational quantum tori and the structure of their automorphism group},
  author = {Karl-Hermann Neeb},
  journal= {arXiv preprint arXiv:math/0511263},
  year   = {2007}
}

Comments

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