Purely Infinite, Simple $C^*$-Algebras Arising from Free Product Constructions, II
نویسندگان
چکیده
منابع مشابه
Purely Infinite Simple C-algebras Arising from Free Product Constructions
Examples of simple, separable, unital, purely infinite C–algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of C∗–algebras by any of a certain class of non–unital endomorphisms; (3) those that arise as reduced free products of pairs of C–algebras with respect to any from a certain class of states...
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In the reduced free product of C∗–algebras, (A, φ) = (A1, φ1) ∗ (A2, φ2) with respect to faithful states φ1 and φ2, A is purely infinite and simple if A1 is a reduced crossed product B ⋊α,r G for G an infinite group, if φ1 is well behaved with respect to this crossed product decomposition, if A2 6= C and if φ is not a trace. The reduced free product construction for C–algebras was invented inde...
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Let Γ = G1 ∗G2 ∗ ... ∗Gn ∗ ... be a free product of at least two but at most countably many cyclic groups. With each such group Γ we associate a family of C*-algebras, denoted C∗ r (Γ,PΛ) and generated by the reduced group C*-algebra C∗ r Γ and a collection PΛ of projections onto the `2-spaces over certain subsets of Γ. We determine W ∗(Γ,PΛ), the weak closure of C∗ r (Γ,PΛ) in L(`2(Γ)), and us...
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In this paper we study the problem of when the corona algebra of a non-unital C∗-algebra is purely infinite. A complete answer is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the algebra, and to the beha...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2002
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-14362