Finite and Torsion Kk-theories
نویسنده
چکیده
We develop a finite KK-theory of C∗-algebras following ArlettazH.Inassaridze’s approach to finite algebraic K-theory [1] . 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 KK-theories. Such bivariant K-theory has almost all KK-theory properties and one has the following exact sequence · · · → KK n (A, B) → KK G n (A, B;Q) → KK G n (A, B;T) → · · · relating KK-theory, rational bivariant K-theory and torsion KK-theory. For a given homology theory on the category of separable GC -algebras finite, rational and torsion homology theories are introduced and investigated. In particular, we formulate finite, torsion and rational versions of Baum-Connes Conjecture. The later is equivalent to the investigation of rational and q-finite analogues for Baum-Connes Conjecture for all prime q.
منابع مشابه
From torsion theories to closure operators and factorization systems
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
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