Journal article
A groupoid generalisation of Leavitt path algebras
Semigroup forum, Vol.89(3), pp.501-517
12/01/2014
DOI: 10.1007/s00233-014-9594-z
Abstract
Let G be a locally compact, Hausdorff, etale 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 C-c(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).
Details
- Title: Subtitle
- A groupoid generalisation of Leavitt path algebras
- Creators
- Lisa Orloff Clark - University of OtagoCynthia Farthing - Department of MathematicsAidan Sims - University of WollongongMark Tomforde - University of Houston
- Resource Type
- Journal article
- Publication Details
- Semigroup forum, Vol.89(3), pp.501-517
- Publisher
- SPRINGER
- DOI
- 10.1007/s00233-014-9594-z
- ISSN
- 0037-1912
- eISSN
- 1432-2137
- Number of pages
- 17
- Grant note
- 210035 / Simons Foundation
- Language
- English
- Date published
- 12/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984240871102771
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