K-theory

Gene Abrams, Pere Ara, Mercedes Siles Molina

Research output: Chapter in BookChapterResearchpeer-review

Abstract

© Springer-Verlag London Ltd. 2017. In this chapter we investigate many of the K-theoretic properties of LK(E). We start by considering the Grothendieck group K0(LK(E)), and then subsequently the Whitehead group K1(LK(E)). Next, we discuss one of the central currently-unresolved questions in the subject (the so-called Algebraic Kirchberg Phillips Question) which asks whether certain K0 data is sufficient to classify the purely infinite simple unital Leavitt path algebras up to isomorphism. We conclude with a discussion of tensor products of Leavitt path algebras, and Hochschild homology.
Original languageEnglish
Title of host publicationLecture Notes in Mathematics
Pages219-257
Number of pages38
Volume2191
DOIs
Publication statusPublished - 1 Jan 2017

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