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Crossed products and twisted k-graph algebras

Journal Article


Abstract

  • An automorphism β of a k-graph Λ induces a crossed product C⋆(Λ)⋊βZ which is isomorphic to a (k+1)-graph algebra C⋆(Λ×βZ). In this paper we show how this process interacts with k-graph C⋆- algebras which have been twisted by an element of their second co-homology group. This analysis is done using a long exact sequence in cohomology associated to this data. We conclude with some examples.

UOW Authors

  •   Brownlowe, Nathan D. (external author)
  •   Deaconu, Valentin (external author)
  •   Kumjian, Alexander (external author)
  •   Pask, David

Publication Date

  • 2016

Citation

  • Brownlowe, N., Deaconu, V., Kumjian, A. & Pask, D. (2016). Crossed products and twisted k-graph algebras. The New York Journal of Mathematics, 22 229-250.

Scopus Eid

  • 2-s2.0-84960398465

Ro Metadata Url

  • http://ro.uow.edu.au/eispapers/5319

Number Of Pages

  • 21

Start Page

  • 229

End Page

  • 250

Volume

  • 22

Place Of Publication

  • http://nyjm.albany.edu/j/2016/22-10v.pdf

Abstract

  • An automorphism β of a k-graph Λ induces a crossed product C⋆(Λ)⋊βZ which is isomorphic to a (k+1)-graph algebra C⋆(Λ×βZ). In this paper we show how this process interacts with k-graph C⋆- algebras which have been twisted by an element of their second co-homology group. This analysis is done using a long exact sequence in cohomology associated to this data. We conclude with some examples.

UOW Authors

  •   Brownlowe, Nathan D. (external author)
  •   Deaconu, Valentin (external author)
  •   Kumjian, Alexander (external author)
  •   Pask, David

Publication Date

  • 2016

Citation

  • Brownlowe, N., Deaconu, V., Kumjian, A. & Pask, D. (2016). Crossed products and twisted k-graph algebras. The New York Journal of Mathematics, 22 229-250.

Scopus Eid

  • 2-s2.0-84960398465

Ro Metadata Url

  • http://ro.uow.edu.au/eispapers/5319

Number Of Pages

  • 21

Start Page

  • 229

End Page

  • 250

Volume

  • 22

Place Of Publication

  • http://nyjm.albany.edu/j/2016/22-10v.pdf