Classification of irreversible and reversible Pimsner operator algebras
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Classification of irreversible and reversible Pimsner operator algebras. / Dor-On, Adam; Eilers, Søren; Geffen, Shirly .
In: Compositio Mathematica, Vol. 156, 2020, p. 2510-2535.Research output: Contribution to journal › Journal article › Research › peer-review
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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