A1-homotopy invariants of corner skew Laurent polynomial algebras

TL;DR

This paper investigates the A1-homotopy invariants of corner skew Laurent polynomial algebras, providing structural insights and computing mod-l algebraic K-theory of Leavitt path algebras through incidence matrices.

Contribution

It introduces new structural properties of A1-homotopy invariants and computes algebraic K-theory of Leavitt path algebras using incidence matrix kernels and cokernels.

Findings

Structural properties of A1-homotopy invariants established

Computed mod-l algebraic K-theory of Leavitt path algebras

Identified vanishing and divisibility properties in algebraic K-theory

Abstract

In this note we prove some structural properties of all the A1-homotopy invariants of corner skew Laurent polynomial algebras. As an application, we compute de 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 algebraic K-theory of these algebras.