Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255345 | Journal of Geometry and Physics | 2018 | 22 Pages |
Abstract
We discuss necessary conditions for a compact quantum group to act on the algebra of noncommutative n-torus Tθn in a filtration preserving way in the sense of Banica and Skalski. As a result, we construct a family of compact quantum groups Gθ=(Aθn,Î) such that for each θ, Gθ is the final object in the category of all compact quantum groups acting on Tθn in a filtration preserving way. We describe in detail the structure of the C*-algebra Aθn
and provide a concrete example of its representation in bounded operators. Moreover, we show that Aθn is isomorphic to the C*-completed version of an algebra of multiple noncommutative torus. Finally, we compute the Haar measure of Gθ
and discuss its representation theory. For θ=0, the quantum group G0 is nothing but the classical group TnâSn, where Sn is the symmetric group.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
MichaÅ Banacki, Marcin Marciniak,