Coverings of skew-products and crossed products by coactions

David Pask, John Quigg, Aidan Sims

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Consider a projective limit G of finite groups Gn. Fix a compatible family n of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction of G on A. We show that the coaction crossed product of A by is isomorphic to a direct limit of the coaction crossed products of A by the n. If A=C*() for some k-graph , and if the coactions n correspond to skew-products of , then we can say more. We prove that the coaction crossed product of C*() by may be realized as a full corner of the C*-algebra of a (k+1)-graph. We then explore connections with Yeends topological higher-rank graphs and their C*-algebras.

Original languageEnglish (US)
Pages (from-to)379-398
Number of pages20
JournalJournal of the Australian Mathematical Society
Volume86
Issue number3
DOIs
StatePublished - Jun 2009
Externally publishedYes

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Coaction
Skew Product
Crossed Product
Covering
C*-algebra
Graph in graph theory
Projective Limit
Direct Limit
Finite Group
Isomorphic

Keywords

  • C*-algebra
  • Coaction
  • Covering
  • Crossed-product
  • Graph algebra
  • K-graph.

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Coverings of skew-products and crossed products by coactions. / Pask, David; Quigg, John; Sims, Aidan.

In: Journal of the Australian Mathematical Society, Vol. 86, No. 3, 06.2009, p. 379-398.

Research output: Contribution to journalArticle

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