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Journal of Lie Theory 14 (2004), No. 1, 199--213
Copyright Heldermann Verlag 2004

H4(BK, Z) and Operator Algebras

Doug Pickrell
Department of Mathematics, University of Arizona, Tucson, AR 85721, U.S.A., Pickrell@math.arizona.edu

There is a well-known interpretation of group cohomology in terms of (generalized) group extensions. For a connected semisimple compact Lie group K, we prove that the extensions corresponding to classes in H4(BK, Z) can be interpreted in terms of automorphisms of a pair consisting of a type II1 von Neumann algebra and a Cartan subalgebra.

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