Concept

Lie groupoid

Publications associées (9)

The representation theory of finite sets and correspondences

We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functor ...

2015

Dirac Optimal Reduction

Tudor Ratiu, Madeleine Jotz

The purpose of this paper is to generalize the (Poisson) Optimal Reduction Theorem in Ortega and Ratiu [Momentum Maps and Hamiltonian Reduction. Progress in Mathematics 222. Boston, MA: Birkhauser. xxxiv, 497pp., 2004] to general proper Lie group actions o ...

Oxford University Press2013

The Leaf Space Of A Multiplicative Foliation

Madeleine Jotz

We show that if a smooth multiplicative subbundle S subset of T G on a groupoid G P is involutive and satisfies completeness conditions, then its leaf space G/S inherits a groupoid structure over the space of leaves of TP boolean AND S in P. As an applicat ...

Amer Inst Mathematical Sciences2012

Invariant frames for vector bundles and applications

Tudor Ratiu, Madeleine Jotz

This paper completes a proof of the Dirac reduction theorem by involutive tangent subbundles. As a consequence, Dirac reduction by a proper Lie group action having one isotropy type is carried out. The main technical tool in the proof is the notion of part ...

Springer Verlag2012

ON THE QUATERNIONIC p-ADIC L-FUNCTIONS ASSOCIATED TO HILBERT MODULAR EIGENFORMS

Jeanine Marie Van Order

We construct p-adic L-functions associated to cuspidal Hilbert modular eigenforms of parallel weight two in certain dihedral or anticyclotomic extensions via the Jacquet-Langlands correspondence, generalizing works of Bertolini-Darmon, Vatsal and others. T ...

2012

Dirac Group(oid)s and Their Homogeneous Spaces

Madeleine Jotz

A theorem of Drinfel'd (Drinfel'd (1993)) classifies the Poisson homogeneous spaces of a Poisson Lie group (G,πG) via a special class of Lagrangian subalgebras of the Drinfel'd double of its Lie bialgebra. This result is extended in Liu et al. (1998) to a ...

EPFL2011

On Singular Poisson Sternberg Spaces

We obtain a theory of stratified Sternberg spaces thereby extending the theory of cotangent bundle reduction for free actions to the singular case where the action on the base manifold consists of only one orbit type. We find that the symplectic reduced sp ...

2009

Some applications of symmetries in differential geometry and dynamical systems

Oana Mihaela Dragulete

This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...

EPFL2007

Symmetry breaking in mechanical systems

The first part of this thesis studies the problem of symmetry breaking in the context of simple mechanical systems with compact symmetry Lie group G. In this part we shall assume that the principal stratum of the G-action on the configuration space Q of a ...

EPFL2005