Toeplitz algebras and the Heisenberg groups

06.06.2025, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Clément Cren (Universität Göttingen)

There is a known link between the creation and annihilation operators on the one hand and the shift operators on a symmetric Fock space on the other. The first give rise to a representation of the Heisenberg group while the later define a Toeplitz algebra. I will explain how this link can be promoted to a an isomorphism between an algebra constructed from the Toeplitz algebra through crossed products and a subalgebra of the C*-algebra of the Heisenberg group. If time permits I will mention some generalizations, either on contact manifolds or for other nilpotent groups.