Diagonal-preserving ring *-isomorphisms of Leavitt path algebras

TL;DR

This paper establishes a precise correspondence between topological isomorphisms of graph groupoids and diagonal-preserving ring *-isomorphisms of Leavitt path algebras, linking algebraic and topological graph invariants.

Contribution

It proves that graph groupoids are topologically isomorphic if and only if their Leavitt path algebras are diagonally *-isomorphic, revealing a new algebraic-topological equivalence.

Findings

Graph groupoids are topologically isomorphic iff their Leavitt path algebras are diagonally *-isomorphic.

Diagonal-preserving ring *-isomorphisms characterize topological graph equivalences.

The result bridges algebraic and topological classifications of directed graphs.

Abstract

The graph groupoids of directed graphs are topologically isomorphic if and only if there is a diagonal-preserving ring *-isomorphism between the Leavitt path algebras.