Event Detail

In his landmark 1993 paper, Kirchberg introduced a property of C*-algebras called the QWEP, which stands for “quotient of the weak expectation property.” As the name suggests, the property is defined by the fact that the algebra is a quotient of a C*-algebra with the weak expectation property, which was a property introduced by Lance years earlier in connection with the theory of tensor products of C*-algebras. While at first glance this seems to be a strange property, Kirchberg showed that whether or not every C*-algebra has the QWEP is equivalent to the famous Connes Embedding Problem (CEP) from von Neumann algebra theory. The CEP remained open for nearly 50 years until its recent refutation in 2020 via a result in quantum complexity theory (as well as the equivalence with Kirchberg’s QWEP conjecture).

Several years ago, I showed that the QWEP is an axiomatizable property of C*-algebras. In this talk, I will present joint work with Aruseelan and Hart where we show that the QWEP does not have an effective axiomatization and, in fact, there can be no effectively axiomatizable satisfiable theory of C*-algebras all of whose models have the QWEP (modulo some nontrivially conditions). The proofs use the connection with the quantum complexity results mentioned above as well as other techniques from C*-algebra theory.