Phase spaces related to standard classical $r$-matrices

Abstract

Fundamental representations of real simple Poisson Lie groups are Poisson actions with a suitable choice of the Poisson structure on the underlying (real) vector space. We study these (mostly quadratic) Poisson structures and corresponding phase spaces (symplectic groupoids).

20 pages, LaTeX, no figures

References in corpus (1)

• Reality in the Differential Calculus on q-euclidean Spaces

Cited by in corpus (7)

• What a classical r-matrix really is
• Poisson-Lie analogues of spin Sutherland models
• Free motion on the Poisson SU(n) group
• Quantum Lorentz and braided Poincare groups
• A decoupling property of some Poisson structures on ${\mathrm{Mat}}_{n\times d}(\mathbb{C})\times {\mathrm{Mat}}_{d\times n}(\mathbb{C})$ supporting $\mathrm{GL}(n,\mathbb{C})\times \mathrm{GL}(d,\mathbb{C})$ Poisson-Lie symmetry
• The semi-direct product of Poisson $G$-spaces
• On braided Poisson and quantum inhomogeneous groups