caa a22 4500 386307180 CHVBK 20180307111533.0 cr unu---uuuuu 161130e198810 xx s 000 0 eng 10.1017/S1446788700030160 doi S1446788700030160 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700030160 Sutherland Colin E. Mathematics Department The University of New South Wales P.O. Box 1 Kensington, N.S.W. 2033, Australia Cartan subalgebras of regular extensions of von Neumann algebras [Elektronische Daten] [Colin E. Sutherland] We analyse the structure of a regular extension γ, υ Q of a von Neumann algebra by an action (modulo inner automorphisms) γ of a discrete group Q, and a nonabelian 2-cycle υ for γ, under the assumption that the "action” γ of Q is cocycle conjugate to an "action”, α which leaves globally invariant a cartan subalgebra of . we show that γ, υ Q is isomorphic with the algebra of the left regular projective representation of a certain discrete, non-principal groupoid V Q determined by the action of Q on the given cartan subalgebrs, where is the Takesaki relation associated to the pair (, ) we apply this description to give a decomposition of the regular representation of a group G into irreducibles, where G is a split extension of a type I group K by an abelian group Q, and work out the details of the author's earlier abstract plancherel theorem in the case when K is abelian. Copyright © Australian Mathematical Society 1988 46 L 10 nationallicence 22 D 25 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 45/2(1988-10), 249-274 1446-7887 45:2<249 1988 45 JAZ https://doi.org/10.1017/S1446788700030160 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700030160 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sutherland Colin E. Mathematics Department The University of New South Wales P.O. Box 1 Kensington, N.S.W. 2033, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/2(1988-10), 249-274 1446-7887 45:2<249 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge