Bivariant K-theory of generalized Weyl algebras

Julio Gutiérrez; Christian Valqui

doi:10.4171/JNCG/375

Bivariant K-theory of generalized Weyl algebras

Julio Gutiérrez, Christian Valqui

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We compute the isomorphism class in KK^alg of all noncommutative generalized Weyl algebras A D C[h].σ; P /, where σ.h/ D qh C h₀ is an automorphism of C[h], except when q ¤ 1 is a root of unity. In particular, we compute the isomorphism class in KK^alg of the quantum Weyl algebra, the primitive factors Bλ of U.sl₂/ and the quantum weighted projective lines O.W P_q.k; l//.

Original language	English
Pages (from-to)	639-666
Number of pages	28
Journal	Journal of Noncommutative Geometry
Volume	14
Issue number	2
DOIs	https://doi.org/10.4171/JNCG/375
State	Published - 2020
Externally published	Yes

Keywords

Generalized Weyl algebras
K-theory
Kk-theory
Smooth generalized crossed products

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10.4171/JNCG/375

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title = "Bivariant K-theory of generalized Weyl algebras",

abstract = "We compute the isomorphism class in KKalg of all noncommutative generalized Weyl algebras A D C[h].σ; P /, where σ.h/ D qh C h0 is an automorphism of C[h], except when q ¤ 1 is a root of unity. In particular, we compute the isomorphism class in KKalg of the quantum Weyl algebra, the primitive factors Bλ of U.sl2/ and the quantum weighted projective lines O.W Pq.k; l//.",

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author = "Julio Guti{\'e}rrez and Christian Valqui",

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journal = "Journal of Noncommutative Geometry",

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AU - Valqui, Christian

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PY - 2020

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N2 - We compute the isomorphism class in KKalg of all noncommutative generalized Weyl algebras A D C[h].σ; P /, where σ.h/ D qh C h0 is an automorphism of C[h], except when q ¤ 1 is a root of unity. In particular, we compute the isomorphism class in KKalg of the quantum Weyl algebra, the primitive factors Bλ of U.sl2/ and the quantum weighted projective lines O.W Pq.k; l//.

AB - We compute the isomorphism class in KKalg of all noncommutative generalized Weyl algebras A D C[h].σ; P /, where σ.h/ D qh C h0 is an automorphism of C[h], except when q ¤ 1 is a root of unity. In particular, we compute the isomorphism class in KKalg of the quantum Weyl algebra, the primitive factors Bλ of U.sl2/ and the quantum weighted projective lines O.W Pq.k; l//.

KW - Generalized Weyl algebras

KW - K-theory

KW - Kk-theory

KW - Smooth generalized crossed products

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DO - 10.4171/JNCG/375

M3 - Article

AN - SCOPUS:85091630103

SN - 1661-6952

VL - 14

SP - 639

EP - 666

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 2

ER -

Bivariant K-theory of generalized Weyl algebras

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