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Finite Dimensional Approximations And Deformations Of Group C*-Algebras, Andrew James Schneider

Open Access Dissertations

Quasidiagonality is a finite-dimensional approximation property of a C*-algebra which indicates that it has matricial approximations that capture the structure of the C*-algebra. We investigate when C*-algebras associated to discrete groups have such a property with particular emphasis on finding obstructions. In particular, we point out that groups with Kazhdan's Property (T) and only finitely many unitary equivalence classes of finite dimensional representations do not produce quasidiagonal C*-algebras. We then observe and note interactions with Property (T) and other approximation properties.

Property (QH) is a related but stronger approximation property with deep connections to E-Theory and …