Kunal Mukherjee

KMS quantum symmetric states

Let A be a unital C∗-algebra and let σ be a one-parameter automorphism group of A. We consider QSSσ(A), the set of all quantum symmetric states on ∗ 1 ∞ A that are also KMS states (for a fixed inverse temperature, for specificity taken to be −1) for the free product automorphism group ∗ 1 ∞ σ . We characterize the elements of QSSσ(A), we show that QSSσ(A) is a Choquet simplex whenever it is nonempty and we characterize its extreme points.

E0-semigroups of free Araki-Woods factors

Analyzing endomorphisms and shift E0-semigroups of free products of von Neumann algebras, we construct uncountably many pairwise cocycle inequivalent E0-semigroups on a large class of free Araki-Woods factors. These E0-semigroups are equimodular but not modularly extendable. We also produce conjugate but not cocycle equivalent E0-semigroups on non-type I factors.