Graded C*-algebras, graded K-theory, and twisted P-graph C*-algebras

Alex Kumjian; David Pask; Aidan Sims

Graded C-algebras, graded K-theory, and twisted P-graph C-algebras

Operator Algebras 2017-06-05 v1 K-Theory and Homology

Authors: Alex Kumjian , David Pask , Aidan Sims

Abstract

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.

Keywords

graded C*-algebras graded K-theory Kasparov theory twisted P-graph C*-algebras Pimsner exact sequence Hilbert bimodules

Cite

@article{arxiv.1706.00563,
  title  = {Graded C*-algebras, graded K-theory, and twisted P-graph C*-algebras},
  author = {Alex Kumjian and David Pask and Aidan Sims},
  journal= {arXiv preprint arXiv:1706.00563},
  year   = {2017}
}

Comments

39 pages, pictures prepared in TikZ