K-theory

Gene Abrams; Pere Ara; Mercedes Siles Molina

doi:10.1007/978-1-4471-7344-1_6

K-theory

Gene Abrams, Pere Ara, Mercedes Siles Molina

Department of Mathematics

Research output: Chapter in Book › Chapter › Research › peer-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 language	English
Title of host publication	Lecture Notes in Mathematics
Pages	219-257
Number of pages	38
Volume	2191
DOIs	https://doi.org/10.1007/978-1-4471-7344-1_6
Publication status	Published - 1 Jan 2017

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Abrams, G., Ara, P., & Siles Molina, M. (2017). K-theory. In Lecture Notes in Mathematics (Vol. 2191, pp. 219-257) https://doi.org/10.1007/978-1-4471-7344-1_6

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AB - © 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.

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