DOCUMENTA MATHEMATICA, Vol. 22 (2017), 423-454

Rasmus Bentmann, Ralf Meyer

A More General Method to Classify up to Equivariant KK-Equivalence

Using a homological invariant together with an obstruction class in a certain \(\Ext2\)-group, we classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results for actions of the circle group on \(\Cst\)\nb-algebras, \(\Cst\)\nb-algebras over finite unique path spaces, and graph \(\Cst\)\nb-algebras with finitely many ideals.

2010 Mathematics Subject Classification: Primary 46L35; Secondary 18E30, 19K35

Keywords and Phrases: Classification, non-simple \(\Cst\)\nb-algebras, K\nb-theory, KK\nb-theory

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