Pinsker Algebras for 1-bounded Entropy
I will discuss the notion of a Pinkser algebra for 1-bounded entropy (a modification of free entropy dimension for strongly 1-bounded algebras in the sense of Jung). Given a tracial von Neumann algebra M, a Pinsker algebra in M is a subalgebra P of M which is maximal with respect to the property that the 1-bounded entropy of P in M is zero. Such algebras always exist. I will discuss properties of Pinkser algebras, as well as give at least one interesting example of such an algebra, and discuss the difficulties involved in producing more examples.