On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups
Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 261-282
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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.
Mots-clés :
16S35, quantum torus, normal form, automorphisms of quantum tori
Neeb, Karl-Hermann. On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups. Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 261-282. doi: 10.4153/CMB-2008-027-7
@article{10_4153_CMB_2008_027_7,
author = {Neeb, Karl-Hermann},
title = {On the {Classification} of {Rational} {Quantum} {Tori} and the {Structure} of {Their} {Automorphism} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {261--282},
year = {2008},
volume = {51},
number = {2},
doi = {10.4153/CMB-2008-027-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-027-7/}
}
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