Local Equivalence of Representations of $${{\rm Diff}^+(S^1)}$$ Diff + ( S 1 ) Corresponding to Different Highest Weights

Restricting positive energy representations of Diff + ( S 1 ) to the stabilizer of n points

Restricting positive energy representations of Diff + ( S 1 ) to the stabilizer of n points

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

RIEMANNIAN GEOMETRY OF Diff(S)/S AND REPRESENTATIONS OF THE VIRASORO ALGEBRA

The main result of the paper is a computation of the Ricci curvature of Diff(S)/S. Unlike earlier results on the subject, we do not use the Kähler structure symmetries to compute the Ricci curvature, but rather rely on classical finite-dimensional results of Nomizu et al on Riemannian geometry of homogeneous spaces. Table of

EXTENSION OF HÖLDER ’ S THEOREM IN Diff 1 + + ( I )

We prove that if Γ is subgroup of Diff 1+ + (I) and N is a natural number such that every non-identity element of Γ has at most N fixed points then Γ is solvable. If in addition Γ is a subgroup of Diff +(I) then we can claim that Γ is metaabelian. It is a classical result (essentially due to Hölder, cf.[N]) that if Γ is a subgroup of Homeo+(R) such that every nontrivial element acts freely then...