1996/02/01 by Anton Alekseev, Anton Yu. Alekseev, Alekseev, Anton Yu. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #dg-ga #math.DG #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.dg-ga/9602001
LaTeX file, 16 pages
arxiv created 1996/02/01 · openalex publication_date 1996/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G_¶ be a compact simple Poisson-Lie group equipped with a Poisson structure ¶ and (M, ø) be a symplectic manifold. Assume that M carries a Poisson action of G_¶ and there is an equivariant moment map in the sense of Lu and Weinstein which acts to the dual Poisson-Lie group G^*_¶, \m: M→ G^*_¶. We prove that M always possesses another symplectic form → so that the G-action preserves ø and there is a new moment map μ= e-1 ∘ \m: M→ \g^*. Here e is a universal (independent of M) invertible equivariant map e: \g^*→ G^*_¶. We suggest new short proves of the convexity theorem for the Poisson-Lie moment map, Poisson reduction theorem and the Ginzburg-Weinstein theorem on the isomorphism of \g^* and G^*_¶ as Poisson spaces.