Publication

Singular Reduction Of Dirac Structures

Tudor Ratiu, Madeleine Jotz
2011
Journal Articles

Résumé

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.

Source officielle

https://infoscience.epfl.ch/entities/publication/88790046-4562-43b9-b65a-7cd214dc4a95

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Tudor Ratiu, Madeleine Jotz
2011
Journal Articles

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/88790046-4562-43b9-b65a-7cd214dc4a95

À propos de ce résultat

Concepts associés (17)

Groupe de Lie

En mathématiques, un groupe de Lie est un groupe qui est aussi une variété différentielle. D'une part, un groupe est une structure algébrique munie d'une opération binaire, typiquement une multiplication et son inverse la division, ou alors une addition et son inverse la soustraction. D'autre part, une variété est un espace qui localement ressemble à un espace euclidien. Ici, on s'intéresse à un ensemble qui est à la fois un groupe et une variété : nous pouvons multiplier les éléments entre eux, calculer l'inverse d'un élément.

Simple Lie group

In mathematics, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symmetric spaces. Together with the commutative Lie group of the real numbers, , and that of the unit-magnitude complex numbers, U(1) (the unit circle), simple Lie groups give the atomic "blocks" that make up all (finite-dimensional) connected Lie groups via the operation of group extension.

Lie group–Lie algebra correspondence

In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Lie groups that are isomorphic to each other have Lie algebras that are isomorphic to each other, but the converse is not necessarily true. One obvious counterexample is and (see real coordinate space and the circle group respectively) which are non-isomorphic to each other as Lie groups but their Lie algebras are isomorphic to each other.

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Touch and Closeness in Naturally Organized Activities

Countless aspects of touch and closeness have been questioned in an unprecedented way during the recent Covid epidemic. Social practices as banal as greetings were both reflexively and practically challenged and sometimes deeply altered, resulting in painf ...

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Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

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Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...

Academic Press Inc Elsevier Science2023

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