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representations of locally compact groupoids
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Definition 0.1 Let
 be a locally compact (topological) groupoid endowed with a Haar system
 . Then a representation of
 together with the its associated Haar system $\nu$ is defined as a triple
 , where: $\mu$ is a quasi-invariant measure defined over
 ,
 is an analytical, fibered Hilbert space or Hilbert bundle over
 , and
 is a Borelian (or borelian) groupoid morphism whose restriction on
 is the identification map, that is,
 is being identified via $L$ with
 . Thus,
$L(x)= [r(x), \tilde{L}(x), d(x)]$ ,
where $ \tilde{L}(x): \H (d(x)) \longrightarrow \H (r(x))$ is a Hilbert space $ \H $ isomorphism.
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"representations of locally compact groupoids" is owned by bci1.
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Cross-references: isomorphism, map, restriction, groupoid morphism, Hilbert bundle, Hilbert space, measure, quasi-invariant, associated Haar system, representation, Haar system, groupoid, locally compact
There are 2 references to this entry.
This is version 12 of representations of locally compact groupoids, born on 2008-07-26, modified 2008-08-23.
Object id is 10876, canonical name is RepresentationsOfLocallyCompactGroupoids.
Accessed 1111 times total.
Classification:
| AMS MSC: | 55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory) | | | 55P10 (Algebraic topology :: Homotopy theory :: Homotopy equivalences) | | | 55N20 (Algebraic topology :: Homology and cohomology theories :: Generalized homology and cohomology theories) | | | 55N33 (Algebraic topology :: Homology and cohomology theories :: Intersection homology and cohomology) | | | 18D05 (Category theory; homological algebra :: Categories with structure :: Double categories, $2$-categories, bicategories and generalizations) |
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Pending Errata and Addenda
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