14 citations · 34 across the 13 of their papers we have counts for
14 papers · 1 filter
Three explicit examples of Lie 2-groupoids
M. Jotz, L. Mußmächer
This note constructs three explicit classes of Lie -groupoids arising from double Lie groupoids via the bar construction of Artin and Mazur, following a result of Mehta and Tang…
Deformations of ideals in Lie algebras
I. Ermeidis, M. Jotz
This paper develops the deformation theory of Lie ideals. It shows that the smooth deformations of an ideal in a Lie algebra differentiate to cohomology…
On the flows of linear vector fields
M. Jotz
This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It then implies easily the existence of glob…
A geometrisation of -manifolds
Malte Heuer, Madeleine Jotz
This paper proposes a geometrisation of -manifolds of degree as -fold vector bundles equipped with a (signed) -symmetry. More precisely, it proves an equival…
Foliated groupoids and their infinitesimal data
Madeleine Jotz, Cristian Ortiz
In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicativ…
The leaf space of a multiplicative foliation
Madeleine Jotz
We show that if a smooth multiplicative subbundle on a groupoid $G\rr P$ is involutive and satisfies completeness conditions, then its leaf space inherits a g…
Infinitesimal objects associated to Dirac groupoids and their homogeneous spaces
M. Jotz
Let $(G\rr P, \mathsf D_G)$ be a Dirac groupoid. We show that there are natural Lie algebroid structures on the units $\lie A(\mathsf D_G)$ and on the core $I^\tg(\mathsf D_G)$ of…
Dirac optimal reduction
Tudor S. Ratiu, Madeleine Jotz
The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A compariso…
Dirac Lie groups, Dirac homogeneous spaces and the Theorem of Drinfeld
Madeleine Jotz
The notions of \emph{Poisson Lie group} and \emph{Poisson homogeneous space} are extended to the Dirac category. The theorem of Drinfeld (\cite{Drinfeld93}) on the one-to-one co…
Invariant generators for generalized distributions
Madeleine Jotz, Tudor S. Ratiu
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
Singular reduction of Dirac structures
Madeleine Jotz, Tudor S. Ratiu, Jedrzej Sniatycki
The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about -invariant vector field…
Hedlund-Metrics and the Stable Norm
Madeleine Jotz
The real homology of a compact Riemannian manifold is naturally endowed with the stable norm. The stable norm on arises from the Riemannian length functiona…
Dirac structures, nonholonomic systems and reduction
Madeleine Jotz, Tudor Ratiu
The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are…
Closedness of the tangent spaces to the orbits of proper actions
Madeleine Jotz, Karl-Hermann Neeb
In this note we show that for any proper action of a Banach--Lie group on a Banach manifold , the corresponding tangent maps $\g \to T_x(M)$ have closed range for each $x \i…