twisted group algebra
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Author(s):  
Federico Bambozzi ◽  
Simone Murro ◽  
Nicola Pinamonti

Abstract For any number $h$ such that $\hbar :=h/2\pi $ is irrational and any skew-symmetric, non-degenerate bilinear form $\sigma :{{\mathbb{Z}}}^{2g}\times{{\mathbb{Z}}}^{2g} \to{{\mathbb{Z}}}$, let be ${{\mathcal{A}}}^h_{g,\sigma }$ be the twisted group *-algebra ${{\mathbb{C}}}[{{\mathbb{Z}}}^{2g}]$ and consider the ergodic group of *-automorphisms of ${{\mathcal{A}}}^h_{g,\sigma }$ induced by the action of the symplectic group $\textrm{Sp} \,({{\mathbb{Z}}}^{2g},\sigma )$. We show that the only $\textrm{Sp} \,({{\mathbb{Z}}}^{2g},\sigma )$-invariant state on ${{\mathcal{A}}}^h_{g,\sigma }$ is the trace state $\tau $.


2008 ◽  
Vol 51 (2) ◽  
pp. 261-282 ◽  
Author(s):  
Karl-Hermann Neeb

AbstractAn n-dimensional quantum torus is a twisted group algebra of the group ℤn. 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.


2001 ◽  
Vol 29 (5) ◽  
pp. 2231-2238 ◽  
Author(s):  
Jairo Z. Gonçalves* ◽  
Arnaldo Mandel†

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