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