We introduce a new construction of E0-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of C0-semigroups. We get a new necessary and sufficient condition for them to be of type III, when the associated sum system is of finite index. Using this criterion, we construct examples of type III E0-semigroups, which can...

We show that the semigroups Sk,` having semigroup presentations 〈a, b : abk = b`a〉 are residually finite and finitely separable. Generally, these semigroups have finite separating images which are finite groups and other finite separating images which are semigroups of order-increasing transformations on a finite partially ordered set. These semigroups thus have vastly different residual and se...

Surprising as it may be at first sight, there are a number of connections between the theories of finite semigroups and dynamical systems, both viewed in a broad sense. For instance in symbolic dynamics, ideas or analogies from the theory of finite automata find a natural setting for application in sofic systems [10, 24] and, even though not usually formulated in dynamical terms, the dynamical ...