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

Neeb, Karl-Hermann

Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 261-282

Résumé

An $n$ -dimensional quantum torus is a twisted group algebra of the group ${{\mathbb{Z}}^{n}}.$ 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.

Détail

DOI : 10.4153/CMB-2008-027-7

Mots-clés : 16S35, quantum torus, normal form, automorphisms of quantum tori

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