2020/04/02 by Tran Giang Nam, Nam, Tran Giang, Jens Zumbrägel +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2004.00889
We investigate the algebra of a Hausdorff ample groupoid, introduced by\nSteinberg, over a commutative semiring S. In particular, we obtain a complete\ncharacterization of congruence-simpleness for such Steinberg algebras,\nextending the well-known characterizations when S is a field or a commutative\nring. We also provide a criterion for the Steinberg algebra of the graph\ngroupoid associated to an arbitrary graph to be congruence-simple. Motivated by\na result of Clark and Sims, we show that, over the Boolean semifield, the\nnatural homomorphism from the Leavitt path algebra to the Steinberg algebra is\nan isomorphism if and only if the associated graph is row-finite. Moreover, we\nestablish the Reduction Theorem and Uniqueness Theorems for Leavitt path\nalgebras of row-finite graphs over the Boolean semifield.\n