Addendum to "Connes' embedding conjecture and sums of Hermitian squares" [Adv. Math. 217 (4) (2008) 1816-1837]

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2014
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Zusammenfassung

We show that Connesʼ embedding conjecture (CEC) is equivalent to a real version of the same (RCEC). Moreover, we show that RCEC is equivalent to a real, purely algebraic statement concerning trace positive polynomials. This purely algebraic reformulation of CEC had previously been given in both a real and a complex version in a paper of the last two authors. The second author discovered a gap in this earlier proof of the equivalence of CEC to the real algebraic reformulation (the proof of the complex algebraic reformulation being correct). In this note, we show that this gap can be filled with help of the theory of real von Neumann algebras.

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510 Mathematik
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Connesʼ embedding problem, Real von Neumann algebras
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ISO 690BURGDORF, Sabine, Ken DYKEMA, Igor KLEP, Markus SCHWEIGHOFER, 2014. Addendum to "Connes' embedding conjecture and sums of Hermitian squares" [Adv. Math. 217 (4) (2008) 1816-1837]. In: Advances in Mathematics. 2014, 252, pp. 805-811. ISSN 0001-8708. eISSN 1090-2082. Available under: doi: 10.1016/j.aim.2013.10.020
BibTex
@article{Burgdorf2014Adden-25764,
  year={2014},
  doi={10.1016/j.aim.2013.10.020},
  title={Addendum to "Connes' embedding conjecture and sums of Hermitian squares" [Adv. Math. 217 (4) (2008) 1816-1837]},
  volume={252},
  issn={0001-8708},
  journal={Advances in Mathematics},
  pages={805--811},
  author={Burgdorf, Sabine and Dykema, Ken and Klep, Igor and Schweighofer, Markus}
}
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