Equivariant Asymptotic Morphisms for the Symplectic Plane
Open Access
Author:
Bakshi, Alok
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
December 06, 2018
Committee Members:
Nigel David Higson, Dissertation Advisor/Co-Advisor Mark Levi, Committee Chair/Co-Chair Paul Frank Baum, Committee Member Nathanial Patrick Brown, Committee Member Martin Bojowald, Outside Member
Keywords:
Quantization Asymptotic Morphism
Abstract:
In this thesis we study equivariant asymptotic morphisms from the
C_0 functions on the symplectic plane into the C*-algebra of compact
operators. We shall construct two asymptotic morphisms that are
asymptotically equivariant for two different groups of symplectomorphisms, and prove (with additional hypotheses) that there does not
exist any asymptotic morphism that is asymptotically equivariant for
all symplectomorphisms. Furthermore, we shall prove that there exists a unique asymptotic morphism (with additional hypothesis on
equivariance) that is equivariant for the group of affine symplectomorphisms of the plane.
