606 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
The -rational -Catalan polynomials for and their -symmetry
We introduce a new statistic, skip, on rational -Dyck paths and define
a marked rank word for each path when is not a multiple of 3. If a triple
of valid statistics (area,skip,dinv) are given, we have an algorithm to
construct the marked rank word corresponding to the triple. By considering all
valid triples we give an explicit formula for the -rational
-Catalan polynomials when . Then there is a natural bijection on the
triples of statistics (area,skips,dinv) which exchanges the statistics area and
dinv while fixing the skip. Thus we prove the -symmetry of
-rational -Catalan polynomials for .Comment: 11 pages, 4 figure
Obstructions to a general characterization of graph correspondences
For a countable discrete space V, every nondegenerate separable
C*-correspondence over c_0(V) is isomorphic to one coming from a directed graph
with vertex set V. In this paper we demonstrate why the analogous
characterizations fail to hold for higher-rank graphs (where one considers
product systems of C*-correspondences) and for topological graphs (where V is
locally compact Hausdorff), and we discuss the obstructions that arise.Comment: major revision; stated some results in greater generalit
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