Leavitt Path Algebras of Hypergraphs

We define Leavitt path algebras of hypergraphs generalizing simultaneously Leavitt path algebras of separated graphs and Leavitt path algebras of vertex-weighted graphs (i.e. weighted graphs that have the property that any two edges emitted by the same vertex have the same weight). We investigate the Leavitt path algebras of hypergraphs in terms of linear bases, Gelfand–Kirillov dimension, ring-theoretic properties (e.g. simplicity, von Neumann regularity and Noetherianess), K -theory and graded K -theory. By doing so we obtain new results on the Gelfand–Kirillov dimension and graded K -theory of Leavitt path algebras of separated graphs and on the graded K -theory of Leavitt path algebras of vertex-weighted graphs.