Graded homotopy classification of Leavitt path algebras

TL;DR

This paper demonstrates that the graded Grothendieck group effectively classifies unital Leavitt path algebras of primitive graphs up to graded homotopy equivalence, advancing algebraic $K$-theory techniques.

Contribution

It introduces new classification methods for Leavitt path algebras using graded algebraic $K$-theory, focusing on homotopy equivalence.

Findings

Graded Grothendieck group classifies unital Leavitt path algebras of primitive graphs.

Development of graded, bivariant algebraic $K$-theory techniques.

Enhanced understanding of algebraic invariants for Leavitt path algebras.

Abstract

We show that the graded Grothendieck group classifies unital Leavitt path algebras of primitive graphs up to graded homotopy equivalence. To this end, we further develop classification techniques for Leavitt path algebras by means of (graded, bivariant) algebraic $K$-theory.