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Coactions and Crossed Products of Hopf C*‐Algebras
Author(s) -
NG ChiKeung
Publication year - 1996
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/s3-72.3.638
Subject(s) - hopf algebra , multiplicative function , mathematics , unitary state , crossed product , pure mathematics , group (periodic table) , algebra over a field , multiplicative group , quantum group , physics , mathematical analysis , quantum mechanics , law , political science
In this paper, we study coactions and their crossed products by Hopf C*‐algebras defined by multiplicative unitaries. We generalize some results in the case of group actions and coactions. Furthermore, when applied to the group case, some of these generalizations improve the original results. For example, we obtained the following result. Let A be a C*‐algebra with coaction ɛ by S where S is a Hopf C*‐algebra defined by an amenable multiplicative unitary. If A is nuclear or C*‐exact, then so is A X ɛ, r Ŝ . This implies that if ( A , G , α ) is any C*‐dynamical system such that A X α, r G is nuclear or C*‐exact, then so is A .