Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665857 | Advances in Mathematics | 2014 | 7 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Sabine Burgdorf, Ken Dykema, Igor Klep, Markus Schweighofer,