KK-theory (original) (raw)
Die KK-Theorie ist eine mathematische Theorie aus dem Bereich der Funktionalanalysis. Der Name rührt daher, dass sie eine K-Theorie mit zwei Variablen darstellt, die die klassische K-Theorie für C*-Algebren und die Theorie der Erweiterungen von C*-Algebren verallgemeinert. Die KK-Theorie geht auf G. G. Kasparow zurück.
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| dbo:abstract | Die KK-Theorie ist eine mathematische Theorie aus dem Bereich der Funktionalanalysis. Der Name rührt daher, dass sie eine K-Theorie mit zwei Variablen darstellt, die die klassische K-Theorie für C*-Algebren und die Theorie der Erweiterungen von C*-Algebren verallgemeinert. Die KK-Theorie geht auf G. G. Kasparow zurück. (de) In mathematics, KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician in 1980. It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of C*-algebras by Lawrence G. Brown, Ronald G. Douglas, and Peter Arthur Fillmore in 1977. In turn, it has had great success in operator algebraic formalism toward the index theory and the classification of nuclear C*-algebras, as it was the key to the solutions of many problems in operator K-theory, such as, for instance, the mere calculation of K-groups. Furthermore, it was essential in the development of the Baum–Connes conjecture and plays a crucial role in noncommutative topology. KK-theory was followed by a series of similar bifunctor constructions such as the E-theory and the , most of them having more category-theoretic flavors, or concerning another class of algebras rather than that of the separable C*-algebras, or incorporating group actions. (en) |
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| rdfs:comment | Die KK-Theorie ist eine mathematische Theorie aus dem Bereich der Funktionalanalysis. Der Name rührt daher, dass sie eine K-Theorie mit zwei Variablen darstellt, die die klassische K-Theorie für C*-Algebren und die Theorie der Erweiterungen von C*-Algebren verallgemeinert. Die KK-Theorie geht auf G. G. Kasparow zurück. (de) In mathematics, KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician in 1980. KK-theory was followed by a series of similar bifunctor constructions such as the E-theory and the , most of them having more category-theoretic flavors, or concerning another class of algebras rather than that of the separable C*-algebras, or incorporating group actions. (en) |
| rdfs:label | KK-Theorie (de) KK-theory (en) |
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