Dressing orbits and a quantum Heisenberg group algebra

*-Representations of a Quantum Heisenberg Group Algebra

In our earlier work, we constructed a specific non-compact quantum group whose quantum group structures have been constructed on a certain twisted group C*-algebra. In a sense, it may be considered as a ``quantum Heisenberg group C*-algebra''. In this paper, we will find, up to equivalence, all of its irreducible *-representations. We will point out the Kirillov type correspondence between the irreducible representations and the so-called ``dressing orbits''. By taking advantage of its comultiplication, we will then introduce and study the notion of ``inner tensor product representations''. We…

海森堡群的 $C^*$-刚性

$C^*$-rigidity of the Heisenberg group

本文证明海森堡群可由其群 $C^*$-代数与其他连通单连通李群区分，关键步骤是利用余伴随轨道的拓扑性质在可解李群中刻画幂零李群。

Isomorphism classes for quantum Heisenberg manifolds

We embed the quantum Heisenberg manifold in a crossed product algebra. This enables us to show that, in the irrational case, all tracial states on $\dc$ induce the same homomorphism on the K_0-group. We conclude that two irrational quantum Heisenberg manifolds $\dc$ and $D^c_{μ' ν'}$ are isomorphic if and only if the parameters $(μ,ν)$ and $(μ',ν')$ belong to the same orbit under the usual action of $GL_2(\ZZ)$ on the torus.

Deformation Quantization for Heisenberg Supergroup

We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d. However, the method used here differs from Rieffel's one: we obtain a Universal Deformation Formula for the actions of R^{m|n} as a byproduct of Weyl ordered Kirillov's orbit method adapted to the graded setting. To do so, we have to introduce the notion of C*-superalgebra, which is compatible with the deformation, and which can be seen as corresponding to noncommutative superspaces. We also use this construction to interpret the renor…