Nondegeneracy of the Lie algebra aff(n)

✍ Scribed by Jean-Paul Dufour; Nguyen Tien Zung

• Book ID: 104447583
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 59 KB
• Volume: 335
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(02)02599-2

✦ Synopsis

We show that aff(n), the Lie algebra of affine transformations of R n , is formally and analytically nondegenerate in the sense of A. Weinstein. This means that every analytic (resp., formal) Poisson structure vanishing at a point with a linear part corresponding to aff(n) is locally analytically (resp., formally) linearizable.