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arXiv · 1907.01366

Classification of irreversible and reversible Pimsner operator algebras

Adam Dor-On·Søren Eilers·Shirly Geffen
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Abstract

Since their inception in the 30's by von Neumann, operator algebras have been used in shedding light in many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two was sought since their emergence in the late 60's. We connect these seemingly separate type of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and $C^*$-algebras with additional $C^*$-algebraic structure. Our approach naturally applies to algebras arising from $C^*$-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.

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Adam Dor-On, Søren Eilers, Shirly Geffen. 2019-07-02. Classification of irreversible and reversible Pimsner operator algebras. https://doi.org/10.1112/s0010437x2000754x

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