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96
Continuous representations of groupoids
, 2007
"... Abstract. We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects, using several examples. We present a palette of results, including, among others: a comparison of the different notions of continuity for r ..."
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Cited by 14 (0 self)
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Abstract. We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects, using several examples. We present a palette of results, including, among others: a comparison of the different notions of continuity
Continuous family groupoids
 Homology, Homotopy and Applications
"... Abstract. In this paper, we define and investigate the properties of continuous family groupoids. This class of groupoids is necessary for investigating the groupoid index theory arising from the equivariant AtiyahSinger index theorem for families, and is also required in noncommutative geometry. T ..."
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Cited by 9 (3 self)
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Abstract. In this paper, we define and investigate the properties of continuous family groupoids. This class of groupoids is necessary for investigating the groupoid index theory arising from the equivariant AtiyahSinger index theorem for families, and is also required in noncommutative geometry
Pseudodifferential Analysis on Continuous Family Groupoids
 DOCUMENTA MATH.
, 2000
"... We study properties and representations of the convolution algebra and the algebra of pseudodifferential operators associated to a continuous family groupoid. We show that the study of representations of the algebras of pseudodifferential operators of order zero completely reduces to the study of ..."
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We study properties and representations of the convolution algebra and the algebra of pseudodifferential operators associated to a continuous family groupoid. We show that the study of representations of the algebras of pseudodifferential operators of order zero completely reduces to the study
Fell Bundles over groupoids
 Proc. Amer. Math. Soc
, 1998
"... A C*algebraic bundle (see [F2, §11]) over a locally compact group may be thought of as a continuous version of a group grading in a C*algebra; one may regard the associated C*algebra as a fairly general sort of crossed product of the fiber algebra over the neutral element by the group (in [LPRS] ..."
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Cited by 26 (4 self)
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A C*algebraic bundle (see [F2, §11]) over a locally compact group may be thought of as a continuous version of a group grading in a C*algebra; one may regard the associated C*algebra as a fairly general sort of crossed product of the fiber algebra over the neutral element by the group (in [LPRS
HAAR SYSTEMS AND HOMOMORPHISMS ON GROUPOIDS
"... Abstract. It is proved that the range map of a locally compact second countable transitive groupoid is open. It is established the equivalence between the continuity of a Haar system and the continuity of certain homomorphisms on groupoid. The results of J. Renault and A.K. Seda concerning the exis ..."
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Abstract. It is proved that the range map of a locally compact second countable transitive groupoid is open. It is established the equivalence between the continuity of a Haar system and the continuity of certain homomorphisms on groupoid. The results of J. Renault and A.K. Seda concerning
Profinite Groupoids and Their Cohomology
"... . We define a notion of profinite groupoid and a suitable class of modules over these. We describe two functors which in the case of a connected profinite groupoid agree; the derived functors of these are the analogues of continuous cohomology of profinite groupoids. The resulting `change of groupoi ..."
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. We define a notion of profinite groupoid and a suitable class of modules over these. We describe two functors which in the case of a connected profinite groupoid agree; the derived functors of these are the analogues of continuous cohomology of profinite groupoids. The resulting `change
REPRESENTATIONS OF ORBIFOLD GROUPOIDS
, 2007
"... Orbifold groupoids have been recently widely used to represent both effective and ineffective orbifolds. We show that every orbifold groupoid can be faithfully represented on a continuous family of finite dimensional Hilbert spaces. As a consequence we obtain the result that every orbifold groupoi ..."
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Orbifold groupoids have been recently widely used to represent both effective and ineffective orbifolds. We show that every orbifold groupoid can be faithfully represented on a continuous family of finite dimensional Hilbert spaces. As a consequence we obtain the result that every orbifold
Continuoustrace groupoid cross products, preprint
, 207
"... Abstract. Let G be a second countable, locally compact groupoid with Haar system, and let A be a bundle of C ∗algebras defined over the unit space of G on which G acts continuously. We determine conditions under which the associated crossed product C ∗ (G; A) is a continuous trace C ∗algebra. 1. ..."
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Cited by 6 (3 self)
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Abstract. Let G be a second countable, locally compact groupoid with Haar system, and let A be a bundle of C ∗algebras defined over the unit space of G on which G acts continuously. We determine conditions under which the associated crossed product C ∗ (G; A) is a continuous trace C ∗algebra. 1.
Groupoid actions as quantale modules
, 2008
"... For an arbitrary localic étale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of Gactions is isomorphic to a corresponding category of O(G)modules, and a ..."
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For an arbitrary localic étale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of Gactions is isomorphic to a corresponding category of O
HAAR SYSTEMS AND TOPOLOGIES ON GROUPOIDS
"... Abstract. For developing an algebraic theory of functions on a locally compact groupoid, one needs an analogue of Haar measure on locally compact groups. This analogue is a system of measures, called Haar system, subject to suitable invariance and smoothness conditions called respectively "left ..."
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;left invariance " and "continuity". Unlike the case of locally compact group, Haar system on groupoid need not exists, and if it does, it will not usually be unique. However on locally compact second countable groupoids one can construct systems of measures satisfying "left invariance "
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