Explicit Rieffel induction module for quantum groups

Rieffel induction as generalized quantum Marsden-Weinstein reduction

A new approach to the quantization of constrained or otherwise reduced classical mechanical systems is proposed. On the classical side, the generalized symplectic reduction procedure of Mikami and Weinstein, as further extended by Xu in connection with symplectic equivalence bimodules and Morita equivalence of Poisson manifolds, is rewritten so as to avoid the use of symplectic groupoids, whose...

Rieffel Type Discrete Deformation of Finite Quantum Groups

We introduce a discrete deformation of Rieffel type for finite (quantum) groups. Using this, we give an example of a finite quantum group A of order 18 such that neither A nor its dual can be expressed as a crossed product of the form C(G1) ⋊τ G2 with G1 and G2 ordinary finite groups. We also give a deformation of finite groups of Lie type by using their maximal abelian subgroups.

Gabor analysis, Rieffel induction and Feichtinger’s algebra as a link

We will show that Feichtinger’s algebra S0(R ) (also known as modulation space M 0 (R ) and well defined for general locally compact Abelian groups) is a natural Hilbert module for quantum tori and that a result by V. Losert can be interpreted as implying that the construction of such Hilbert modules gives Feichtinger’s algebra, if one considers the category of time-frequency invariant homogeno...

Picard Groups for Derived Module Categories

Quantum Error-Correction Codes on Abelian Groups

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.