201 research outputs found
Imprimitivity for -Coactions of Non-Amenable Groups
We give a condition on a full coaction of a (possibly)
nonamenable group and a closed normal subgroup of which ensures
that Mansfield imprimitivity works; i.e. that is
Morita equivalent to A\times_\delta G\times_{\deltahat,r} N. This condition
obtains if is amenable or is normal. It is preserved under Morita
equivalence, inflation of coactions, the stabilization trick of Echterhoff and
Raeburn, and on passing to twisted coactions.Comment: 23 pages, LaTeX 2e, requires amscd.sty and pb-diagram.sty. Revisions
include deletion of false Lemma 2.3 and amendment of proofs of Proposition
2.4 and Theorem 4.1, which had relied on the false lemma or its proo
Rigidity theory for -dynamical systems and the "Pedersen Rigidity Problem", II
This is a follow-up to a paper with the same title and by the same authors.
In that paper, all groups were assumed to be abelian, and we are now aiming to
generalize the results to nonabelian groups.
The motivating point is Pedersen's theorem, which does hold for an arbitrary
locally compact group , saying that two actions and
of are outer conjugate if and only if the dual coactions
and
of are conjugate via an isomorphism that maps the image of onto the
image of (inside the multiplier algebras of the respective crossed
products).
We do not know of any examples of a pair of non-outer-conjugate actions such
that their dual coactions are conjugate, and our interest is therefore
exploring the necessity of latter condition involving the images, and we have
decided to use the term "Pedersen rigid" for cases where this condition is
indeed redundant.
There is also a related problem, concerning the possibility of a so-called
equivariant coaction having a unique generalized fixed-point algebra, that we
call "fixed-point rigidity". In particular, if the dual coaction of an action
is fixed-point rigid, then the action itself is Pedersen rigid, and no example
of non-fixed-point-rigid coaction is known.Comment: Minor revision. To appear in Internat. J. Mat
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