The Algebraic Side of MIP* = RE

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Shows MIP = RE produces a concrete obstruction to Connes embedding by building a finitely presented synchronous game algebra whose relations admit a tracial state but no homomorphism into the ultrapower RU; uses noncommutative polynomial presentations, epsilon representations* (Hilbert–Schmidt norm), the GNS construction, and an ultrafilter ultralimit to form RU. The construction yields a separable finite von Neumann algebra coming from the game that provably fails to embed in RU, giving a strong, explicit counterexample.

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" chapters (17)

1. 0:00Introduction
2. 3:16What is algebra
3. 5:09Homomorphisms
4. 6:00Quotients
5. 8:57Presentation Algebra
6. 11:35Examples
7. 13:20Matrices
8. 15:11Representations
9. 15:31Question
10. 19:06Residually finite dimensional
11. 20:39Epsilon representations
12. 22:51Nonlocal games
13. 25:12Perfect finitedimensional strategies
14. 28:28Approximate representations
15. 33:02If and only if
16. 44:04GS Representation Theorem
17. 50:32Ultra Limits