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Positivity is undecidable in products of free algebras

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

For free -algebras, free group algebras, and related algebras, it is possible to decide if an element is positive (in all representations) using results of Helton, Bakonyi-Timotin, Helton-McCullough, and others. In this talk, I’ll discuss joint work with Arthur Mehta and Yuming Zhao showing that this problem becomes undecidable for tensor products of this algebras. I’ll also discuss how results of this type could be aided by having a Higman embedding theorem for algebras with states, as well as work in progress on this question. This research direction is inspired by the MIP =RE theorem, which can also be understood as showing that a decision problem for operator algebras is undecidable.

This talk is part of the Isaac Newton Institute Seminar Series series.

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