Neumann, Katharina: A description of the Jacobson topology on the spectrum of transformation group C*-algebras by proper actions. 2011
Inhalt
- Introduction
- Definitions and tools
- Proper G-spaces
- Locally compact groups and their representations
- C*-algebras and their representations
- Crossed products and generalized fixed point algebras
- Induced representations of covariant systems
- The space Stab(X) "0362
- Subgroup C*-algebras and subgroup representations
- A topology and a G-action for Stab(X) "0362
- Continuity of `39`42`"613A``45`47`"603AindG
- Stab(X) "0362 for actions with continuous stabilizer map
- Induction via bimodules
- Basic definitions
- The category C
- Inducing representations via bimodules
- The Morita equivalence of C0(GH Y)G and C0(Y)H
- The reduction to the compact case
- Representation theory of compact groups and ideals in L2(K)
- The Peter-Weyl Theorem
- Minimal ideals in L2(K)
- L2(G) as an induced space
- Restriction of continuous elements of L2(K)
- A convergence lemma for nets in Rep(K) with limit in K"0362K
- The map `39`42`"613A``45`47`"603AindG is a homeomorphism
- A C*-algebra with spectrum Stab(X) "0362
- Proper G-spaces with Palais' slice property
- Motivation for the consideration of (SP)
- The topology on Stab(X) "0362 if X satisfies (SP)
- Different settings — different proofs
- Some useful results and complementary proofs
- References