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Journal of Noncommutative Geometry


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Volume 11, Issue 4, 2017, pp. 1627–1643
DOI: 10.4171/JNCG/11-4-12

Published online: 2017-12-15

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

Gonçalo Tabuada[1]

(1) MIT, Cambridge, USA and Universidade Nova de Lisboa, Portugal

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.

Keywords: Corner skew Laurent polynomial algebra, Leavitt path algebra, algebraic $K$-theory, noncommutative mixed motives, noncommutative algebraic geometry

Tabuada Gonçalo: $\mathbb A^1$-homotopy invariants of corner skew Laurent polynomial algebras. J. Noncommut. Geom. 11 (2017), 1627-1643. doi: 10.4171/JNCG/11-4-12