Linear hamiltonian circle actions that generate minimal Hilbert bases

Ágúst Sverrir Egilsson

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 1, page 285-315
  • ISSN: 0373-0956

Abstract

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The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper we consider the question whether among these almost Poisson structures one can find algebras satisfying Jacobi identity. It is shown that this is not the case when the weights of the action satisfy a simple relation. A consequence of this relation is also that the number of generators needed to generate the algebra of invariant functions is minimal.

How to cite

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Egilsson, Ágúst Sverrir. "Linear hamiltonian circle actions that generate minimal Hilbert bases." Annales de l'institut Fourier 50.1 (2000): 285-315. <http://eudml.org/doc/75417>.

@article{Egilsson2000,
abstract = {The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper we consider the question whether among these almost Poisson structures one can find algebras satisfying Jacobi identity. It is shown that this is not the case when the weights of the action satisfy a simple relation. A consequence of this relation is also that the number of generators needed to generate the algebra of invariant functions is minimal.},
author = {Egilsson, Ágúst Sverrir},
journal = {Annales de l'institut Fourier},
keywords = {singular Poisson structure; reduction; Hamiltonian action},
language = {eng},
number = {1},
pages = {285-315},
publisher = {Association des Annales de l'Institut Fourier},
title = {Linear hamiltonian circle actions that generate minimal Hilbert bases},
url = {http://eudml.org/doc/75417},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Egilsson, Ágúst Sverrir
TI - Linear hamiltonian circle actions that generate minimal Hilbert bases
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 1
SP - 285
EP - 315
AB - The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper we consider the question whether among these almost Poisson structures one can find algebras satisfying Jacobi identity. It is shown that this is not the case when the weights of the action satisfy a simple relation. A consequence of this relation is also that the number of generators needed to generate the algebra of invariant functions is minimal.
LA - eng
KW - singular Poisson structure; reduction; Hamiltonian action
UR - http://eudml.org/doc/75417
ER -

References

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