Decomposable approximations and coloured isomorphisms for C*-algebras

In this thesis we introduce nuclear dimension and compare it with a stronger form of the completely positive approximation property. We show that the approximations forming this stronger characterisation of the completely positive approximation property witness finite nuclear dimension if and only if the underlying C*-algebra is approximately finite dimensional. We also extend this result to nuclear dimension at most omega. We review interactions between separably acting injective von Neumann algebras and separable nuclear C*-algebras. In particular, we discuss aspects of Connes' work and how some of his strategies have been used by C^*-algebraist to estimate the nuclear dimension of certain classes of C*-algebras. We introduce a notion of coloured isomorphisms between separable unital C*-algebras. Under these coloured isomorphisms ideal lattices, trace spaces, commutativity, nuclearity, finite nuclear dimension and weakly pure infiniteness are preserved. We show that these coloured isomorphisms induce isomorphisms on the classes of finite dimensional and commutative C*-algebras. We prove that any pair of Kirchberg algebras are 2-coloured isomorphic and any pair of separable, simple, unital, finite, nuclear and Z-stable C*-algebras with unique trace which satisfy the UCT are also 2-coloured isomorphic.

Joseph McKeen and the soul of Bowdoin College: an analysis of the chapel sermons of Rev. Joseph McKeen, first president of Bowdoin College, as they relate to his call to serve the common good

The Reverend Joseph McKeen (1757-1807) was the first president of Bowdoin College, Brunswick, Maine, USA, (founded 1794). McKeen is famous for his inaugural address in which he calls students to serve the common good. His view of common good is a deeply theological view, coloured by the theological era in which he lived and worked. This study examines the idea of common in the light of McKeen’s college sermons, taking note of the following subjects: Scottish Common Sense Realism; The Nature of True Virtue; The Controversy with Unitarianism; and Science and Mathematics. McKeen’s view of common good is not simply a political view. He is not merely a republican, expressing his views on the future of the republic in a classical political way. He is also, indeed primarily, a pastor and theologian.