Cartan subalgebras of regular extensions of von Neumann algebras

Journal of the Australian Mathematical Society

Colin E. Sutherland¹ 

关键词: 46 L 10;    22 D 25;   

DOI  :  10.1017/S1446788700030160

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We analyse the structure of a regular extension ℳ ⋊ γ, υQ of a von Neumann algebra ℳ 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 subalgebraof ℳ. we show that ℳ ⋊ γ, υQ is isomorphic with the algebra of the left regular projective representation of a certain discrete, non-principal groupoid ℜ V Q determined by the action of Q on the given cartan subalgebrs, where ℜ is the Takesaki relation associated to the pair (ℳ, ) 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.

【 授权许可】

Unknown