Oliver Margetts (Lancaster) - "Irreversible dynamics in operator algebras"

Abstract

In this talk we look at one parameter semigroups of *-endomorphisms of operator algebras. We study a nice nontrivial class: the E₀-semigroups. These were introduced by R. Powers in the late 80s as a first step towards defining an analogue of Fredholm index for unbounded derivations. Since then they been related to areas of quantum probability, open quantum systems and quantum field theory. The most significant progress has been for E₀-semigroups on B(H), where there exists a continuum of examples and a relatively simple index theory. On the other hand, for M ≠ B(H) constructing and classifying E₀-semigroups has remained a difficult task. In this talk we take up that challenge for a particular class of algebras, constructing an index and giving a countable of number distinct examples.