Imprimitivity for C-coactions of Non-amenable Groups

نویسندگان

  • S. KALISZEWSKI
  • JOHN QUIGG
چکیده

We give a condition on a full coaction (A,G, δ) of a (possibly) nonamenable group G and a closed normal subgroup N of G which ensures that Mansfield imprimitivity works; i.e. that A×δ| G/N is Morita equivalent to A×δ G×δ̂,r N . This condition obtains if N is amenable or δ is normal. It is preserved under Morita equivalence, inflation of coactions, the stabilization trick of Echterhoff and Raeburn, and on passing to twisted coactions.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Equivariance and Imprimitivity for Discrete Hopf C * -coactions

Let U , V , and W be multiplicative unitaries coming from discrete Kac systems such that W is an amenable normal submultiplica-tive unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of SV andˆSV , their restrictions to SW andˆSU , their dual coactions, and their full and reduced crossed products. If N (A) denotes the imprimitivity bimodule associated to a ...

متن کامل

Crossed Products by Dual Coactions of Groups and Homogeneous Spaces

Mansfield showed how to induce representations of crossed products of C∗algebras by coactions from crossed products by quotient groups and proved an imprimitivity theorem characterising these induced representations. We give an alternative construction of his bimodule in the case of dual coactions, based on the symmetric imprimitivity theorem of the third author; this provides a more workable w...

متن کامل

Morita equivalences between fixed point algebras and crossed products

In this paper, we will prove that if A is a C-algebra with an effective coaction ǫ by a compact quantum group, then the fixed point algebra and the reduced crossed product are Morita equivalent. As an application, we prove an imprimitivity type theorem for crossed products of coactions by discrete Kac C-algebras.

متن کامل

Three Bimodules for Mansfield’s Imprimitivity Theorem

For a maximal coaction δ of a discrete group G on a C-algebra A and a normal subgroup N of G, there are at least three natural A ×δ G δ̂| N − A ×δ| G/N imprimitivity bimodules: Mansfield’s bimodule Y G G/N(A); the bimodule assembled by Ng from Green’s A ×δ G δ̂ G ׈̂ δ| G/N − A ×δ G δ̂| N imprimitivity bimodule X N (A ×δ G) and Katayama duality; and the bimodule assembled from X G N (A ×δ G) and th...

متن کامل

Covariant Representations of Hecke Algebras and Imprimitivity for Crossed Products by Homogeneous Spaces

For discrete Hecke pairs (G,H), we introduce a notion of covariant representation which reduces in the case where H is normal to the usual definition of covariance for the action of G/H on c0(G/H) by right translation; in many cases where G is a semidirect product, it can also be expressed in terms of covariance for a semigroup action. We use this covariance to characterise the representations ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1996