Classification of irreversible and reversible Pimsner operator algebras

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Standard

Classification of irreversible and reversible Pimsner operator algebras. / Dor-On, Adam; Eilers, Søren; Geffen, Shirly .

I: Compositio Mathematica, Bind 156, 2020, s. 2510-2535.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Dor-On, A, Eilers, S & Geffen, S 2020, 'Classification of irreversible and reversible Pimsner operator algebras', Compositio Mathematica, bind 156, s. 2510-2535. https://doi.org/10.1112/S0010437X2000754X

APA

Dor-On, A., Eilers, S., & Geffen, S. (2020). Classification of irreversible and reversible Pimsner operator algebras. Compositio Mathematica, 156, 2510-2535. https://doi.org/10.1112/S0010437X2000754X

Vancouver

Dor-On A, Eilers S, Geffen S. Classification of irreversible and reversible Pimsner operator algebras. Compositio Mathematica. 2020;156:2510-2535. https://doi.org/10.1112/S0010437X2000754X

Author

Dor-On, Adam ; Eilers, Søren ; Geffen, Shirly . / Classification of irreversible and reversible Pimsner operator algebras. I: Compositio Mathematica. 2020 ; Bind 156. s. 2510-2535.

Bibtex

@article{7d3f26d4879947728cefd877df15a264,
title = "Classification of irreversible and reversible Pimsner operator algebras",
abstract = "Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought sincetheir emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and -algebras with additional -algebraic structure. Our approach naturally applies to algebras arising from -correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs. ",
keywords = "classification, graph algebras, K-theory, non-commutative boundary, Pimsner algebras, reconstruction, rigidity, tensor algebras",
author = "Adam Dor-On and S{\o}ren Eilers and Shirly Geffen",
year = "2020",
doi = "10.1112/S0010437X2000754X",
language = "English",
volume = "156",
pages = "2510--2535",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",

}

RIS

TY - JOUR

T1 - Classification of irreversible and reversible Pimsner operator algebras

AU - Dor-On, Adam

AU - Eilers, Søren

AU - Geffen, Shirly

PY - 2020

Y1 - 2020

N2 - Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought sincetheir emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and -algebras with additional -algebraic structure. Our approach naturally applies to algebras arising from -correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs.

AB - Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought sincetheir emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and -algebras with additional -algebraic structure. Our approach naturally applies to algebras arising from -correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs.

KW - classification

KW - graph algebras

KW - K-theory

KW - non-commutative boundary

KW - Pimsner algebras

KW - reconstruction

KW - rigidity

KW - tensor algebras

U2 - 10.1112/S0010437X2000754X

DO - 10.1112/S0010437X2000754X

M3 - Journal article

AN - SCOPUS:85099464068

VL - 156

SP - 2510

EP - 2535

JO - Compositio Mathematica

JF - Compositio Mathematica

SN - 0010-437X

ER -

ID: 255779429