Poisson Manifolds Associated with Group Actions and Classical Triangular r-Matrices

✍ Scribed by P. Xu

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 951 KB
• Volume: 112
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1993.1031

✦ Synopsis

Let (P) be a Poisson (G)-space and (A) a classical triangular (r)-matrix. Using the Poisson reduction, we construct a new Poisson structure (P_{A}) on (P). For this new Poisson structure (P_{1}), we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of (P_{1}) is also discussed. ' 1993 Academic Press. Inc.