### 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 |
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Title of host publication | Lecture Notes in Mathematics |

Pages | 219-257 |

Number of pages | 38 |

Volume | 2191 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

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## Cite this

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