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Skew-products of higher-rank graphs and crossed products by semigroups

Journal Article


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Abstract


  • We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C ∗-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the C ∗-algebra of a quotient graph. Our main tool is Laca’s dilation theory for endomorphic actions of Ore semigroups on C ∗-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger C ∗-algebra.

Authors


  •   Maloney, Benjamin (external author)
  •   Pask, David A.
  •   Raeburn, Iain F. (external author)

Publication Date


  • 2014

Citation


  • Maloney, B., Pask, D. & Raeburn, I. (2014). Skew-products of higher-rank graphs and crossed products by semigroups. Semigroup Forum, 88 (1), 162-176.

Scopus Eid


  • 2-s2.0-84893728979

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3031&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2022

Number Of Pages


  • 14

Start Page


  • 162

End Page


  • 176

Volume


  • 88

Issue


  • 1

Abstract


  • We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C ∗-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the C ∗-algebra of a quotient graph. Our main tool is Laca’s dilation theory for endomorphic actions of Ore semigroups on C ∗-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger C ∗-algebra.

Authors


  •   Maloney, Benjamin (external author)
  •   Pask, David A.
  •   Raeburn, Iain F. (external author)

Publication Date


  • 2014

Citation


  • Maloney, B., Pask, D. & Raeburn, I. (2014). Skew-products of higher-rank graphs and crossed products by semigroups. Semigroup Forum, 88 (1), 162-176.

Scopus Eid


  • 2-s2.0-84893728979

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3031&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2022

Number Of Pages


  • 14

Start Page


  • 162

End Page


  • 176

Volume


  • 88

Issue


  • 1