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Search: All articles in the CMB digital archive with keyword KK-theory

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1. CMB 2015 (vol 58 pp. 374)

Szabó, Gábor
 A Short Note on the Continuous Rokhlin Property and the Universal Coefficient Theorem in $E$-Theory Let $G$ be a metrizable compact group, $A$ a separable $\mathrm{C}^*$-algebra and $\alpha\colon G\to\operatorname{Aut}(A)$ a strongly continuous action. Provided that $\alpha$ satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in $E$-theory passes from $A$ to the crossed product $\mathrm{C}^*$-algebra $A\rtimes_\alpha G$ and the fixed point algebra $A^\alpha$. This extends a similar result by Gardella for $KK$-theory in the case of unital $\mathrm{C}^*$-algebras, but with a shorter and less technical proof. For circle actions on separable, unital $\mathrm{C}^*$-algebras with the continuous Rokhlin property, we establish a connection between the $E$-theory equivalence class of $A$ and that of its fixed point algebra $A^\alpha$. Keywords:Rokhlin property, UCT, KK-theory, E-theory, circle actionsCategories:46L55, 19K35

2. CMB 2010 (vol 54 pp. 68)

Eilers, Søren; Restorff, Gunnar; Ruiz, Efren
 Non-splitting in Kirchberg's Ideal-related $KK$-Theory A. Bonkat obtained a universal coefficient theorem in the setting of Kirchberg's ideal-related $KK$-theory in the fundamental case of a $C^*$-algebra with one specified ideal. The universal coefficient sequence was shown to split, unnaturally, under certain conditions. Employing certain $K$-theoretical information derivable from the given operator algebras using a method introduced here, we shall demonstrate that Bonkat's UCT does not split in general. Related methods lead to information on the complexity of the $K$-theory which must be used to classify $*$-isomorphisms for purely infinite $C^*$-algebras with one non-trivial ideal. Keywords:KK-theory, UCTCategory:46L35
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