On the $K$-theory in splitexact algebraic $KK$-theory
Bernhard Burgstaller
TL;DR
This paper proves that in the universal splitexact equivariant algebraic KK-theory, the K-theory groups align with classical K-theory, addressing a question posed by Kasparov.
Contribution
It establishes the equivalence of algebraic KK-theory K-groups with classical K-theory, providing a partial answer to Kasparov's question.
Findings
K-theory groups in algebraic KK-theory coincide with classical K-theory
Addresses a question raised by Kasparov about the relationship between these theories
Enhances understanding of the structure of equivariant algebraic KK-theory
Abstract
It is proven that in the universal splitexact equivariant algebraic -theory for algebras, the -theory groups coincide with classical -theory in the sense of Phillips. This partially answers a question raised by Kasparov.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models