GeNoCAS 2023: Guido Arnone

Graded homotopy classification of Leavitt path algebras


Leavitt path algebras are a family of (typically) non-commutative algebras constructed from graphs; the notion of length of paths endows them with a canonical grading over the group of integers.

The graded classification conjecture for Leavitt path algebras asserts that the graded Grothendieck group of a Leavitt path algebra can recover its isomorphism type as a graded algebra.

In this talk we will discuss a weaker version of this conjecture, namely, that the graded Grothendieck group classifies LPAs up to a notion of graded polynomial homotopy equivalence. We will show how this conjecture

can be verified for primitive graphs using techniques related to (graded) bivariant K-theory.