$\mathbb A^1$-homotopy invariants of corner skew Laurent polynomial algebras

Abstract

In this note we prove some structural properties of all the $\mathbb A^1$-homotopy invariants of corner skew Laurent polynomial algebras. As an application, we compute the mod-$l$ algebraic $K$-theory of Leavitt path algebras using solely the kernel/cokernel of the incidence matrix. This leads naturally to some vanishing and divisibility properties of the $K$-theory of these algebras.