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arXiv · 1502.05573

Nonclassifiability of UHF $L^p$-operator algebras

Eusebio Gardella·Martino Lupini
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Abstract

We prove that simple, separable, monotracial UHF $L^{p}$-operator algebras are not classifiable up to (complete) isomorphism using countable structures, such as K-theoretic data, as invariants. The same assertion holds even if one only considers UHF $L^{p}$-operator algebras of tensor product type obtained from a diagonal system of similarities. For $p=2$, it follows that separable nonselfadjoint UHF operator algebras are not classifiable by countable structures up to (complete) isomorphism. Our results, which answer a question of N. Christopher Phillips, rely on Borel complexity theory, and particularly Hjorth's theory of turbulence.

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Eusebio Gardella, Martino Lupini. 2015-02-19. Nonclassifiability of UHF $L^p$-operator algebras. https://doi.org/10.1090/proc/12859

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