Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

Maria Joiţa

Open Mathematics (2009)

  • Volume: 7, Issue: 1, page 73-83
  • ISSN: 2391-5455

Abstract

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We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math. Soc. 49(1984), 289–306].

How to cite

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Maria Joiţa. "Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras." Open Mathematics 7.1 (2009): 73-83. <http://eudml.org/doc/269248>.

@article{MariaJoiţa2009,
abstract = {We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math. Soc. 49(1984), 289–306].},
author = {Maria Joiţa},
journal = {Open Mathematics},
keywords = {Group actions; Strong Morita equivalence; Pro-C *-algebras; Hilbert modules; group actions; strong Morita equivalence; pro--algebras},
language = {eng},
number = {1},
pages = {73-83},
title = {Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras},
url = {http://eudml.org/doc/269248},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Maria Joiţa
TI - Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras
JO - Open Mathematics
PY - 2009
VL - 7
IS - 1
SP - 73
EP - 83
AB - We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math. Soc. 49(1984), 289–306].
LA - eng
KW - Group actions; Strong Morita equivalence; Pro-C *-algebras; Hilbert modules; group actions; strong Morita equivalence; pro--algebras
UR - http://eudml.org/doc/269248
ER -

References

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