Quantum Heisenberg manifolds (QHMs) are noncommutative manifolds constructed by Marc Rieffel as a strict deformation quantization of Heisenberg manifolds (in the direction of the Poisson bracket). They are the fibers of a continuous field of noncommutative -algebras , where are parameters of the Poisson bracket, is a positive integer and is the deformation parameter. The QHM is in fact a generalized fixed point algebra of a certain crossed product -algebra by construction and it can be also realized as a crossed product by a Hilbert -bimodule, Cuntz-Pimsner algebra and twisted groupoid -algebra. The goal of this series of lectures is to introduce various types of -algebras and to discuss the structure of the QHM in some details. In the first lecture, we briefly discuss the history and the motivation of deformation quantization, and introduce the QHMs as a strict deformation quantization of Heisenberg manifolds.
Quantum Heisenberg Manifolds
Feb. 23, 2016 2pm (MATH 350)
Lie Theory
Erica Shannon (CU) Some stuff about invariant forms
We will explore the rich combinatorial structure based on set partitions that arises from the supercharacter theory of unipotent upper triangular matrix groups.
Quantum Heisenberg Manifolds