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Lie groups as permutation groups: Ulam's problem in the nilpotent case

Related publications (50)

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Singular Reduction Of Dirac Structures

Tudor Ratiu, Madeleine Jotz

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 G-invariant vector fields and one-forms are shown. ...

2011

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

Noetherian loop spaces

Jérôme Scherer

The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p-compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg-Mac Lane spaces such as ℂP∞ and 3-connected covers of co ...

2011

Generalized Euler-Poincar, Equations on Lie Groups and Homogeneous Spaces, Orbit Invariants and Applications

Feride Tiglay

We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar, equations on Lie groups and homogeneous spaces. Orbit invariants play an impor ...

Springer Netherlands2011

On the bounded cohomology of semi-simple groups, S-arithmetic groups and products

Nicolas Monod

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and gr ...

De Gruyter2010

Differential geometry applied to crystallography

Philippe Kocian

The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...

EPFL2009

Nilpotent subalgebras of semisimple Lie algebras

Donna Testerman

Let g be the Lie algebra of a semisimple linear algebraic group. Under mild conditions on the characteristic of the underlying field, one can show that any subalgebra of g consisting of nilpotent elements is contained in some Borel subalgebra. In this Note ...

2009

Geodesic Vlasov Equations And Their Integrable Moment Closures

Cesare Tronci

Various integrable geodesic flows on Lie groups are shown to arise by taking moments of a geodesic Vlasov equation on the group of canonical transformations. This was already known for both the one- and two-component Camassa-Holm systems [18, 19]. The pres ...

2009

Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions

Cesare Tronci

The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect produ ...

2009

Extended Formulations for Packing and Partitioning Orbitopes

Yuri Faenza

We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in Kaibel and Pfetsch [Kaibel, V., M. E. Pfetsch. 2008. Packing and partitioning orbitopes. Math. Programming ...

2009