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Journals and Conferences
It is proved that algebraic and topological K-functors are isomorphic on the category of stable generalized operator algebras which are Ki-regular for all i > 0. In 1979 Karoubi conjectured the isomorphism of algebraic and topological Kfunctors on the category of stable C-algebras [Ka]. This conjecture was confirmed by Higson for Karoubi-Villamayor… (More)
Kasparov KK-groups KK(A,B) are represented as homotopy groups of the Pedersen-Weibel nonconnective algebraic K-theory spectrum of the additive category of Fredholm (A,B)-bimodules for A and B, respectively, a separable and σ-unital trivially graded real or complex C∗-algebra acted upon by a fixed compact metrizable group.
Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi ⊗̂-stable real (or complex) Fréchet algebras.
A universal C∗-algebra is constructed which is generated by a partial isometry. Using grading on this algebra we construct an analog of Cuntz algebras which gives a homotopical interpretation of KK-groups. It is proved that this algebra is homotopy equivalent up to stabilization by 2×2 matrices to M2(C). Therefore those algebras are KK-isomorphic. We recall… (More)
Let a compact group G act on real or complex C∗-algebras A and B, with A separable and B σ-unital. We express the G-equivariant Kasparov groups KKn(A,B) by algebraic K-groups of a certain additive category.
We give interpretations of some known key agreement protocols in the framework of category theory and in this way we give a method of constructing of many new key agreement protocols.
Higson’s homotopy invariance theorem for complex and real C∗-algebras is proved. Some consequences are derived.
We develop a finite KK-theory of C∗-algebras following ArlettazH.Inassaridze’s approach to finite algebraic K-theory  . The BrowderKaroubi-Lambre’s theorem on the orders of the elements for finite algebraic K-theory [ , ] is extended to finite KK-theory. A new bivariant theory, called torsion KK-theory is defined as the direct limit of finite… (More)