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arXiv · 1110.6198

A groupoid generalization of Leavitt path algebras

Lisa Orloff Clark·Cynthia Farthing·Aidan Sims·Mark Tomforde
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Abstract

Let G be a locally compact, Hausdorff groupoid in which s is a local homeomorphism and the unit space is totally disconnected. Assume there is a continuous cocycle c from G into a discrete group $Γ$. We show that the collection A(G) of locally-constant, compactly supported 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).

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Lisa Orloff Clark, Cynthia Farthing, Aidan Sims, Mark Tomforde. 2012-02-06. A groupoid generalization of Leavitt path algebras. https://arxiv.org/abs/1110.6198

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