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Covariant Representations for Coactions of Hopf C*‐Algebras
Author(s) -
Conti Roberto,
Wang Shuzhou
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001625
Subject(s) - mathematics , covariant transformation , multiplicative function , pure mathematics , hopf algebra , unitary state , tensor product , crossed product , subalgebra , unitary representation , invariant (physics) , algebra over a field , unital , mathematical physics , lie group , mathematical analysis , political science , law
Given a coaction α of a Hopf C*‐algebra A on a C*‐algebra B with an α‐invariant C*‐subalgebra C , and a conditional expectation E : B → C commuting with α, it is shown that if (π, u ) is a covariant representation of the system ( C , A , α∣ C ), then there is an associated covariant representation( π ˜ , u ˜ )of the system ( B , A , α), where π ˜is the representation induced from π up to B via E , andu ˜is a unitary corepresentation of A naturally associated with u . Some applications are also discussed, including a lifting of ergodic coactions to von Neumann algebras, and a characterization of the amenability of multiplicative unitary operators via infinite tensor product covariant representations. 2000 Mathematics Subject Classification 46L55, 46L60, 46L87, 46L89, 81R15, 81R50, 81T05.