# Leavitt path algebras of hypergraphs

## TL;DR

This paper introduces a new class of Leavitt path algebras for hypergraphs, extending existing frameworks, and explores their algebraic properties, K-theory, and dimensions, providing new insights into their structure.

## Contribution

It defines Leavitt path algebras of hypergraphs, generalizing previous models, and analyzes their algebraic and K-theoretic properties, including bases, dimensions, and regularity.

## Key findings

- Linear bases for the algebras are found.
- Gelfand-Kirillov dimension is computed.
- Results on simplicity, regularity, and Noetherian properties are obtained.

## Abstract

We define Leavitt path algebras of hypergraphs generalizing simultaneously Leavitt path algebras of finitely separated graphs and Leavitt path algebras of row-finite vertex-weighted graphs. We find linear bases for those algebras, compute their Gelfand-Kirillov dimension, obtain some results on ring-theoretic properties like simplicity, von Neumann regularity and Noetherianess and investigate their 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 weighted Leavitt path algebras.