- 04-330 Hendrik Grundling
- Generalising Group Algebras
Oct 22, 04
(auto. generated ps),
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Abstract. We generalise group algebras to algebraic objects with bounded Hilbert
space representation theory - the generalised group algebras are called
"host" algebras. The main property of a host algebra, is that its
representation theory should be isomorphic (in the sense of the
Gelfand--Raikov theorem) to a specified subset of representations of
the algebraic object.
Here we obtain both existence and uniqueness theorems for host algebras
as well as general structure theorems for host algebras.
Abstractly, this solves the question of when a set of Hilbert space
representations is isomorphic to the representation theory of a C*-algebra.
To make contact with harmonic analysis, we consider general convolution
algebras associated to representation sets, and consider conditions
for a convolution algebra to be a host algebra.