The Connes embedding problem is a major open question in the theory of von Neumann algebras, formulated by the French mathematician Alain Connes in the 1970s. It remains one of the central unresolved problems in operator algebra theory.
Facts
StatementConnes' embedding problem asks whether every type II1 factor on a separable Hilbert space can be embedded into some R^omega. 1 Progress Toward ResolutionIn January 2020, Ji, Natarajan, Vidick, Wright, and Yuen announced a result in quantum complexity theory that implies a negative answer to Connes' embedding problem. 1 Classification
Resolution Status Chronology
Resolved Year Prize Status
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In Branch
Source Connes Embedding Problem, Wikipedia
Posed By
Source Connes Embedding Problem, Wikipedia
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1. Connes Embedding Problem, Wikipedia
Statement section
Connes' embedding problem asks whether every type II1 factor on a separable Hilbert space can be embedded into some R^omega.
Introduction section
In January 2020, Ji, Natarajan, Vidick, Wright, and Yuen announced a result in quantum complexity theory that implies a negative answer to Connes' embedding problem.
In Branch: Operator Theory, Lead section
by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory. During that time, the problem was reformulated
Posed By: Alain Connes, Lead section
Connes' embedding problem, formulated by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory.
View the Source2. Connes embedding problem (Wikipedia)
In January 2020, Ji, Natarajan, Vidick, Wright, and Yuen announced a result in quantum complexity theory that implies a negative answer to Connes' embedding problemView the Source Reader Challenges (0)
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