On isomorphic classical diffeomorphism groups, III

1995 ◽  
Vol 13 (2) ◽  
pp. 117-127 ◽  
Author(s):  
Augustin Banyaga ◽  
Andrew McInerney
Keyword(s):  
Diffeomorphism Groups

scholarly journals Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

2013 ◽  
Vol 77 (3) ◽  
pp. 109-138 ◽  
Author(s):  
Mario Micheli ◽  
Mario Micheli ◽  
П Михор ◽  
Peter W Michor ◽  
Давид Мамфорд ◽  
...  
Keyword(s):  
Diffeomorphism Groups ◽  
Derived Geometry

scholarly journals QUASI-SIMPLICITY OF SOME HOMEOMORPHISM AND DIFFEOMORPHISM GROUPS

2010 ◽  
Vol 43 (1) ◽  
Author(s):  
Agnieszka Kowalik ◽  
Ilona Michalik
Keyword(s):  
Diffeomorphism Groups

scholarly journals Positive energy representations of Sobolev diffeomorphism groups of the circle

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Sebastiano Carpi ◽  
Simone Del Vecchio ◽  
Stefano Iovieno ◽  
Yoh Tanimoto
Keyword(s):  
Unitary Representation ◽  
Von Neumann Algebras ◽  
Universal Covering ◽  
Irreducible Representations ◽  
Positive Energy ◽  
Diffeomorphism Groups ◽  
Von Neumann ◽  
Direct Sum ◽  
Covering Groups

AbstractWe show that any positive energy projective unitary representation of $$\mathrm{Diff}_+(S^1)$$ Diff + ( S 1 ) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) for any real $$s>3$$ s > 3 , and in particular to $$C^k$$ C k -diffeomorphisms $$\mathrm{Diff}_+^k(S^1)$$ Diff + k ( S 1 ) with $$k\ge 4$$ k ≥ 4 . A similar result holds for the universal covering groups provided that the representation is assumed to be a direct sum of irreducibles. As an application we show that a conformal net of von Neumann algebras on $$S^1$$ S 1 is covariant with respect to $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) , $$s > 3$$ s > 3 . Moreover every direct sum of irreducible representations of a conformal net is also $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) -covariant.

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