We describe the C∗-algebra of an E-unitary or strongly 0-E-unitary inverse semigroup as the partial crossed product of a commutative C∗-algebra by the maximal group image of the inverse semigroup. We give a similar result for the C∗-algebra of the tight groupoid of an inverse semigroup. We also study conditions on a groupoid C∗-algebra to be Morita equivalent to a full crossed product of a commutative C∗-algebra with an inverse semigroup, generalizing results of Khoshkam and Skandalis for crossed products with groups.
1
The University of Texas at Tyler, USA
2
City College of New York, USA
David Milan; Benjamin Steinberg. On inverse semigroup $C^*$-algebras and crossed products. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 485-512. doi: 10.4171/ggd/236
@article{10_4171_ggd_236,
author = {David Milan and Benjamin Steinberg},
title = {On inverse semigroup $C^*$-algebras and crossed products},
journal = {Groups, geometry, and dynamics},
pages = {485--512},
year = {2014},
volume = {8},
number = {2},
doi = {10.4171/ggd/236},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/236/}
}
TY - JOUR
AU - David Milan
AU - Benjamin Steinberg
TI - On inverse semigroup $C^*$-algebras and crossed products
JO - Groups, geometry, and dynamics
PY - 2014
SP - 485
EP - 512
VL - 8
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/236/
DO - 10.4171/ggd/236
ID - 10_4171_ggd_236
ER -
%0 Journal Article
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%J Groups, geometry, and dynamics
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%V 8
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/236/
%R 10.4171/ggd/236
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