منابع مشابه
Integrability and Reduction of Poisson Group Actions 1
In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group G with dual G⋆ we obtain a suitably connected integrating symplectic double groupoid S. As a consequence, the cotangent lift of a Poisson action on an integrable Poisson manifold P can be integrated to a Poisson actio...
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The Hopf algebra of Feynman diagrams, analyzed by A.Connes and D.Kreimer, is considered from the perspective of the theory of effective actions and generalized τ-functions, which describes the action of diffeomorphism and shift groups in the moduli space of coupling constants. These considerations provide additional evidence of the hidden group (integrable) structure behind the standard formali...
متن کاملIntegrability and Reduction of Hamiltonian Actions on Dirac Manifolds
For a Hamiltonian, proper and free action of a Lie group G on a Dirac manifold (M,L), with a regular moment map μ :M → g∗, the manifolds M/G, μ−1(0) and μ−1(0)/G all have natural induced Dirac structures. If (M,L) is an integrable Dirac structure, we show thatM/G is always integrable, but μ−1(0) and μ−1(0)/G may fail to be integrable, and we describe the obstructions to their integrability.
متن کاملGroup Actions
The symmetric groups Sn, alternating groups An, and (for n ≥ 3) dihedral groups Dn behave, by their very definition, as permutations on certain sets. The groups Sn and An both permute the set {1, 2, . . . , n} and Dn can be considered as a group of permutations of a regular n-gon, or even just of its n vertices, since rigid motions of the vertices determine where the rest of the n-gon goes. If ...
متن کاملGroup Actions
There are a number of results of group theory presented in Herstein [1] (the counting principles in Sections 2.5 and 2.11, Cayley’s theorem in Section 2.9 and the Sylow theorems of Section 2.12, among others) whose proofs follow similar ideas. However, it is not apparent that this is so. This handout covers the ideas necessary to tie these results together. The important idea is that of an acti...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2009
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-009-0348-x