A groupoid generalisation of Leavitt path algebras

作者：Clark Lisa Orloff^*; Farthing Cynthia; Sims Aidan; Tomforde Mark

来源：Semigroup Forum, 2014, 89(3): 501-517.

DOI：10.1007/s00233-014-9594-z

• Topological groupoids
• Leavitt algebra
• Groupoid algebra
• Graded algebra

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).

• 出版日期2014-12