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C*‐Algèbres De Kac Et Algèbres De Kac
Author(s) -
Enock Michel,
Vallin Jean-Michel
Publication year - 1993
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-66.3.619
Subject(s) - mathematics , converse , pure mathematics , von neumann algebra , c* algebra , commutative property , invariant (physics) , algebra over a field , von neumann architecture , algebra representation , jordan algebra , mathematical physics , geometry
S. Baaj and G. Skandalis have proved that, to every Kac algebra, as studied by J.‐M. Schwartz and the first author, corresponds a canonical C*‐Kac algebra, as studied by the second author. This article proves the converse result. So, we have then a complete proof that the C* version and the von Neumann version of this theory are exactly equivalent, as are, in the commutative case, thanks to A. Weil's theorem, locally compact groups and measured groups with a left‐invariant measure.
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