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arXiv · 2203.05710

An Index for Inclusions of Operator Systems

Roy Araiza·Colton Griffin·Thomas Sinclair
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Abstract

Inspired by a well-known characterization of the index of an inclusion of II$_1$ factors due to Pimsner and Popa, we define an index-type invariant for inclusions of operator systems. We compute examples of this invariant, show that it is multiplicative under minimal tensor products, and explain how it generalizes the quantum Lov\'asz theta invariant for a matricial system defined by Duan, Severini, and Winter.

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Roy Araiza, Colton Griffin, Thomas Sinclair. 2022-03-11. An Index for Inclusions of Operator Systems. https://arxiv.org/abs/2203.05710

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