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Call No.	Ph.D. 2009
Author	Goehle, Geoff.
Title	Groupoid crossed products.
Date	2009
Abstract	We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian stabilizers and a well behaved orbit space. In this case, the spectrum of the crossed product is homeomorphic, via an induction map, to a quotient of the spectrum of the crossed product by the stabilizer group bundle. The main theorem is also generalized in the groupoid algebra case to an identification of the primitive ideal space. This generalization replaces the assumption that the orbit space is well behaved with an amenability hypothesis. We then use induction to show that the primitive ideal space of the groupoid algebra is homeomorphic to a quotient of the dual of the stabilizer group bundle. In both cases the identification is topological. We then apply these theorems in a number of examples, and examine when a groupoid algebra has Hausdorff spectrum. As a separate result, we also develop a theory of principal groupoid group bundles and locally unitary groupoid actions. We prove that such actions are characterized, up to exterior equivalence, by a cohomology class which arises from a principal bundle. Furthermore, we also demonstrate how to construct a locally unitary action from a given principal bundle. This last result uses a duality theorem for abelian group bundles which is also included as part of this thesis.
Description	xi, 492 leaves : ill. 28 cm.
Format	application/pdf
Advisor	Williams, Dana, Muhly, Paul, Webb, David, Trout, John
Subject	Groupoids. Crossed products. Abelian groups.
College	Dartmouth College -- Department of Mathematics.
Issuing Body	Dartmouth Dissertations are made available through the Dartmouth Digital Library.
Degree	Thesis (Ph.D.)--Dartmouth College.
Copyright	All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means without permission in writing from the author.
DOI	http://dx.doi.org/10.1349/ddlp.263

Title	Page 1
Format	application/pdf
Issuing Body	Dartmouth Dissertations are made available through the Dartmouth Digital Library.
Degree	Thesis (Ph.D.)--Dartmouth College.
Full Text	GROUPOID CROSSED PRODUCTS A Thesis Submitted to the Faculty in partial ful llment of the requirements for the degree of Doctor of Philosophy in Mathematics by Geo Goehle DARTMOUTH COLLEGE Hanover, New Hampshire May 29, 2009 Examining Committee: Dana Williams, Chair Paul Muhly John Trout David Webb Brian W. Pogue, Ph.D. Dean of Graduate Studies

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Groupoid crossed products.

Groupoid crossed products.