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

Gonçalo Tabuada

doi:10.4171/jncg/11-4-12

JournalsjncgVol. 11, No. 4pp. 1627–1643

$A^{1}$ -homotopy invariants of corner skew Laurent polynomial algebras

Gonçalo Tabuada
MIT, Cambridge, USA and Universidade Nova de Lisboa, Portugal

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Abstract

In this note we prove some structural properties of all the $A^{1}$ -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.

Cite this article

Gonçalo Tabuada, $A^{1}$ -homotopy invariants of corner skew Laurent polynomial algebras. J. Noncommut. Geom. 11 (2017), no. 4, pp. 1627–1643

DOI 10.4171/JNCG/11-4-12