Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 23 for “"Groupoid"”.
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Groupoid Models of Irrational Rotation Algebras
We show how to construct certain groupoid models of irrational rotation algebras and show how this can be used to to find projections in the algebra.
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A groupoid approach to geometric mechanics
… or incompressible, irrotational or not. By using groupoids we generalize Arnold’s diffeomorphism group framework for fluid flows to show that the well-known equations governing the motion of these various systems can be viewed as geodesic equations (or more generally, Newton’s equations) written …
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Duistermaat-Heckman measures for Hamiltonian groupoid actions
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms
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The Baum-Connes Map for a Smooth Groupoid
… map is extended to the case of any smooth groupoid. Then we prove that the Baum-Connes map is invariant under the groupoid equivalence.
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Homology, cohomology and extensions of ordered groupoids
… homology, cohomology and extensions of ordered groupoids. We study the simplicial homology of ordered groupoids. We also discuss the (co)homology of the set of identities of ordered groupoids and relate the cohomology of the set of identities of an ordered groupoid to the cohomology of the …
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Steinberg algebra and Leavitt path algebras
… susceptible to a new approach using topological groupoids. Taking a special kind of groupoid G, one can construct an R-algebra called the Steinberg algebra of G. Many interesting classes of algebras, including Leavitt path algebras, can be obtained from this process. This dissertation is an …
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GT-shadows related to finite quotients of the full modular group
… V. Drinfeld in 1990 [5]. GT-shadows [4] form a groupoid whose objects are certain finite index normal subgroups of Artin’s braid group B4 on 4 strands. In this thesis we introduce GT-shadows for the gentle version GTgen of the Grothendieck-Teichmueller group. These entities are morphisms of a …
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Connections between binary systems and admissible topologies
Let G = (a,b,c,...) be a groupoid and T a topology for G with U<sub>a</sub> denoting an open set in T that contains the element a. The topology T is admissible for G if for every a·b=c and U<sub>c</sub> there exist U<sub>a</sub> and U<sub>b</sub> such that U<sub>a</sub>·U<sub>b</sub> c …
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Parabolic Springer resolution
… be a parabolic subgroup. We construct a functor Groupoid ... is a connected space, which induces an action of generalizing a classical result. It is also a part of a study of natural equivalences between ... for P, Q associated parabolic subgroups.
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Lie Theory in Generalized Kähler Geometry
… Morita equivalences of symplectic double groupoids, 2-morphisms between Morita equivalences, and multiplicative LS bisections in order to access the underlying holomorphic data, and smooth data associated with GK structures. We then employ techniques from Poisson Geometry, such as gauge …
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Partial dynamical systems and AF C*-algebras
… utilizing the connections between C*-algebras, groupoids, and inverse semigroups, we obtain a characterization theorem, in terms of dynamical systems, of approximately finite-dimensional (AF) C*-algebras. The dynamical systems considered in this characterization consist of partially defined …
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Stacks in Poisson geometry
… the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The second chapter discusses standard concepts in …
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Foliations and exotic index theory
… on compact manifolds, the corona of the holonomy groupoid is a fiber bundle over the ambient manifold whose fiber is the corona of the universal leaf. By this property, an idea in the work of S. Hurder can be applied to Riemannian foliations on a compact manifold to show that the analytic assembly …
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Symplectic foliations, currents, and local Lie groupoids
… calibrated symplectic foliations, and local Lie groupoids. Calibrated symplectic foliations are one possible generalization of taut foliations of 3-manifolds to higher dimensions. Their study has been popular in recent years, and we collect several interesting results. We then show how de Rham’s …
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partial translation algebras for certain discrete metric spaces
… We also examine a way to form a groupoid from a partial translation<br/>structure, and prove that in the case of a discrete group the associated<br/>C*-algebra is the same as the reduced group C*-algebra. In addition to<br/>this we present several subsidiary results relating to …
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Continuous and discrete aspects of Lagrangian field theories with nonholonomic constraints
… discrete field theories taking values in Lie groupoids. It is shown that many previously known discrete field theories are particular instances of Lie groupoid field theories, and the geometry of Lie groupoids is used to construct a unifying framework for this class. In two further chapters, …
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On the Finite Axiomatizability of Equational Theories of Automatic Algebras
… in an algebraic way to give us a type of groupoid, which we call an automatic algebra. Automatic algebras are of interest because, unlike groups and rings, among finite automatic algebras there are examples, already in the literature, of finitely based algebras, inherently nonfinitely …
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Relating Thompson's group V to graphs of groups and Hecke algebras
… are Steinberg algebras of a particular \'{e}tale groupoid. Finally we show that certain unitaries in $L_K(\mathcal{G})$ form a group we can understand as a variant of Thompson's $V$, combining features of both Nekrashevych-R\"{o}ver groups and Matui's topological full groups of one-sided shifts. …
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Ideals and Maximal Commutative Subrings of Graded Rings
… graded rings and (under some conditions) groupoid crossed products, each nonzero ideal of the ring has a nonzero intersection with the commutant of the center of the neutral component subring. In particular, if the neutral component subring is maximal commutative in the ring this yields …
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Abelianization of groupoids and Lie algebroids
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms
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