Continuous representations of groupoids

Details Continuous representations of groupoids Continuous representations of groupoids

2006-12-21

arxiv.org/abs/math/0612639v3

Mathematics

Representation Theory

41 pages

Scientific paper

We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects and discuss some of the standard constructions from representation theory in this particular context. An important r\^{ole} is played by the regular representation. We conclude by discussing some operator algebra associated to continuous representations of groupoids; in particular, we analyse the relationship of continuous representations of $G$ and continuous representations of the Banach $*$-category $\hat{L}^{1}(G)$.

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