On the coadjoint Virasoro action

Abstract

The set of coadjoint orbits of the Virasoro algebra at level 1 is in bijection with the set of conjugacy classes in a certain open subset $\widetilde{\mathrm{SL}}(2,\mathbb{R}{)}_{+}$ of the universal cover of $\mathrm{SL}(2,\mathbb{R})$. We strengthen this bijection to a Morita equivalence of quasi-symplectic groupoids, integrating the Poisson structure on ${\mathfrak{vir}}_1^{\ast }(S^1)$ and the Cartan-Dirac structure on $\widetilde{\mathrm{SL}}(2,\mathbb{R}{)}_{+}$, respectively.

40 pages

References in corpus (1)

• Group-valued momentum maps for actions of automorphism groups

Cited by in corpus (2)

• Symplectic geometry of Teichmüller spaces for surfaces with ideal boundary
• Shifted coisotropic structures for differentiable stacks