Reduction of Poisson algebras at nonzero momentum values

✍ Scribed by Judith Arms

• Book ID: 104343380
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 628 KB
• Volume: 21
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(96)00009-5

✦ Synopsis

A reduction of a Poisson manifold using the ideal 1 (J) generated by the momentum map was introduced by Sniatycki and Weinstein (1983). This reduction has been extended to nonzero momentum values # by two methods: by shifting to zero momentum on a larger space, the product with the coadjoint orbit; and by the method of Wilbour and Kimura (1991, 1993) using the modified ideal 1 (J -/~). It is shown that these two methods produce isomorphic reduced algebras under the assumptions that the symmetry group is connected and that the stabilizer group of/~ also is connected. If the latter assumption fails, the shifted reduced algebra is isomorphic to a (possibly proper) subalgebra of the Wilbour-Kimura algebra.