Compatible quadratic Poisson brackets related to a family of elliptic curves

Please always quote using this URN: urn:nbn:de:0297-zib-16097
  • We construct nine pairwise compatible quadratic Poisson structures such that a generic linear combination of them is associated with an elliptic algebra in $n$ generators. Explicit formulas for Casimir elements of this elliptic Poisson structure are obtained.

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Author:Alexander Odesskii, Thomas Wolf
Document Type:ZIB-Report
MSC-Classification:14-XX ALGEBRAIC GEOMETRY
17-XX NONASSOCIATIVE RINGS AND ALGEBRAS
32-XX SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES (For infinite-dimensional holomorphy, see 46G20, 58B12)
Date of first Publication:2012/10/16
Series (Serial Number):ZIB-Report (12-31)
ArXiv Id:http://arxiv.org/abs/1204.1299
ISSN:1438-0064
Published in:To appear in (accepted): Journal of Geometry and Physics