Abstract
This paper is an outgrowth of joint work with Richard Herman [5] and Iain Raeburn [13]. In both of these projects, questions concerning group actions on operator algebras naturally led to a study of obstruction classes in H2(G,U(A)), where U(A) is the (suitably topologized) unitary group of an abelian operator algebra A. The appropriate cohomology theory here is the “Borel cochain” theory of C.C.Moore, as developed and systematized in [8]. In case A is a von Neumann algebra, U(A) is essentially what Moore calls U(X,T) (X here is some standard measure space), and machinery for computing the relevant cohomology groups is developed and applied in [8] and [9].
Research supported in part by NSF Grants DMS-8400900 and 8120790.
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Rosenberg, J. (1986). Some Results on Cohomology with Borel Cochains, with Applications to Group Actions on Operator Algebras. In: Douglas, R.G., Pearcy, C.M., Sz.-Nagy, B., Vasilescu, FH., Voiculescu, D., Arsene, G. (eds) Advances in Invariant Subspaces and Other Results of Operator Theory. Operator Theory: Advances and Applications, vol 17. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7698-8_22
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