Purely infinite crossed products by endomorphisms
نویسندگان
چکیده
منابع مشابه
Purely infinite partial crossed products
Let (A, G, alpha) be a partial dynamical system. We show that there is a bijective corespondence between Ginvariant ideals of A and ideals in the partial crossed prroduct A xalpha, r G provided the action is exact and residually topologically free.
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We study C*-algebra endomorphims which are special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts. We assign to such endomorphisms a geometrical invariant, representing a cohomological obstruction for them to be special in the usual sense. Moreover, we construct the crossed product of a C*-algebra by the action of the dual of a (nonabelian, noncompact) group of vector b...
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C*-algebra endomorphisms arising from superselection structures with non-trivial centre define a ’rank’ and a ’first Chern class’. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the above-mentioned rank and first Chern class, and can be used to construct a duality for abstract (nonsymmetric) tensor categories vs. group bundles acting on (nonsy...
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We construct the crossed product A ⋊ ρ̂ of a C*-algebra A with centre Z by an endomorphism ρ , which is special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts; the notation ρ̂ denotes the tensor C*-category of powers of ρ . We assign to ρ a geometrical invariant, representing a cohomological obstruction for it to be special in the usual sense; such invariant determines ra...
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Let I+ be the positive cone in a totally ordered abelian group F. We construct crossed products by actions of J+ as endomorphisms of C*algebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C*-algebras generated by two semigroups V, W: I+ -+ B(H) of nonunitary isometrics are canonically isomorphic, thus giving a new, sel...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.10.078