2017/06/02 by Alex Kumjian, Kumjian, Alex, David Pask +3
Mathematics · #19K35 #46L05 #Advanced Operator Algebra Research #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1706.00563
openalex publication_date 2017/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish graded versions of Pimsner's six-term sequences for graded Hilbert bimodules whose left action is injective and by compacts, and a graded Pimsner-Voiculescu sequence. We introduce the notion of a twisted P-graph C*-algebra and establish connections with graded C*-algebras. Specifically, we show how a functor from a P-graph into the group of order two determines a grading of the associated C*-algebra. We apply our graded version of Pimsner's exact sequence to compute the graded K-theory of a graph C*-algebra carrying such a grading.