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 SL˜(2,R)+ of the universal cover of SL(2,R). We strengthen this bijection to a Morita equivalence of quasi-symplectic groupoids, integrating the Poisson structure on vir1⁎(S1) and the Cartan-Dirac structure on SL˜(2,R)+, respectively.
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