Publication

Dirac Optimal Reduction

Tudor Ratiu, Madeleine Jotz
2013
Journal Articles

Abstract

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 on Dirac manifolds, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reduction.

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https://infoscience.epfl.ch/entities/publication/a2866bf9-f5f3-4a1d-ad66-a694104835fb

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Tudor Ratiu, Madeleine Jotz
2013
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a2866bf9-f5f3-4a1d-ad66-a694104835fb

About this result

Related concepts (13)

Lie group

In mathematics, a Lie group (pronounced liː ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction).

Group action

In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.

Semisimple Lie algebra

In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero proper ideals). Throughout the article, unless otherwise stated, a Lie algebra is a finite-dimensional Lie algebra over a field of characteristic 0. For such a Lie algebra , if nonzero, the following conditions are equivalent: is semisimple; the Killing form, κ(x,y) = tr(ad(x)ad(y)), is non-degenerate; has no non-zero abelian ideals; has no non-zero solvable ideals; the radical (maximal solvable ideal) of is zero.

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