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Crossed Products of C*‐Algebras by Semigroups of Automorphisms
Author(s) -
Murphy Gerard J.
Publication year - 1994
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/s3-68.2.423
Subject(s) - automorphism , crossed product , mathematics , covariant transformation , pure mathematics , simple (philosophy) , product (mathematics) , representation (politics) , representation theory , irreducible representation , automorphisms of the symmetric and alternating groups , algebra over a field , mathematical physics , epistemology , geometry , political science , law , philosophy , politics
Extending the usual theory of crossed products by discrete groups, a theory of crossed products of C*‐algebras by semigroups of their automorphisms is developed. The representation theory is analysed and conditions are given for when covariant representations of a C*‐dynamical system give rise to faithful and/or irreducible representations of the corresponding crossed product. These results are used to give conditions ensuring that the crossed product is simple or primitive.