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

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© 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.

Idioma original	Anglès
Títol de la publicació	Lecture Notes in Mathematics
Pàgines	219-257
Nombre de pàgines	38
Volum	2191
DOIs	https://doi.org/10.1007/978-1-4471-7344-1_6
Estat de la publicació	Publicada - 1 de gen. 2017

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

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title = "K-theory",

abstract = "{\textcopyright} 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.",

author = "Gene Abrams and Pere Ara and {Siles Molina}, Mercedes",

year = "2017",

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day = "1",

doi = "10.1007/978-1-4471-7344-1_6",

language = "English",

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volume = "2191",

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booktitle = "Lecture Notes in Mathematics",

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T1 - K-theory

AU - Abrams, Gene

AU - Ara, Pere

AU - Siles Molina, Mercedes

PY - 2017/1/1

Y1 - 2017/1/1

N2 - © 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.

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.

U2 - 10.1007/978-1-4471-7344-1_6

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M3 - Chapter

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VL - 2191

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EP - 257

BT - Lecture Notes in Mathematics

ER -

K-theory

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