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A groupoid generalisation of Leavitt path algebras

Journal Article


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Abstract


  • Let G be a locally compact, Hausdorff, étale groupoid whose unit space is totally disconnected. We show that the collection A(G) of locally-constant, compactly supported complex-valued functions on G is a dense ∗ -subalgebra of Cc(G) and that it is universal for algebraic representations of the collection of compact open bisections of G . We also show that if G is the groupoid associated to a row-finite graph or k -graph with no sources, then A(G) is isomorphic to the associated Leavitt path algebra or Kumjian–Pask algebra. We prove versions of the Cuntz–Krieger and graded uniqueness theorems for A(G) .

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Farthing, Cynthia (external author)
  •   Sims, Aidan
  •   Tomforde, Mark (external author)

Publication Date


  • 2014

Citation


  • Clark, L. Orloff., Farthing, C., Sims, A. & Tomforde, M. (2014). A groupoid generalisation of Leavitt path algebras. Semigroup Forum, 89 (3), 501-517.

Scopus Eid


  • 2-s2.0-84988419987

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3331&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2322

Has Global Citation Frequency


Number Of Pages


  • 16

Start Page


  • 501

End Page


  • 517

Volume


  • 89

Issue


  • 3

Place Of Publication


  • United States

Abstract


  • Let G be a locally compact, Hausdorff, étale groupoid whose unit space is totally disconnected. We show that the collection A(G) of locally-constant, compactly supported complex-valued functions on G is a dense ∗ -subalgebra of Cc(G) and that it is universal for algebraic representations of the collection of compact open bisections of G . We also show that if G is the groupoid associated to a row-finite graph or k -graph with no sources, then A(G) is isomorphic to the associated Leavitt path algebra or Kumjian–Pask algebra. We prove versions of the Cuntz–Krieger and graded uniqueness theorems for A(G) .

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Farthing, Cynthia (external author)
  •   Sims, Aidan
  •   Tomforde, Mark (external author)

Publication Date


  • 2014

Citation


  • Clark, L. Orloff., Farthing, C., Sims, A. & Tomforde, M. (2014). A groupoid generalisation of Leavitt path algebras. Semigroup Forum, 89 (3), 501-517.

Scopus Eid


  • 2-s2.0-84988419987

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3331&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2322

Has Global Citation Frequency


Number Of Pages


  • 16

Start Page


  • 501

End Page


  • 517

Volume


  • 89

Issue


  • 3

Place Of Publication


  • United States