Coordinates for triangular operator algebras. II

Introduction to vertex operator algebras II

This is the second of three lectures on introduction to vertex operator algebras. In this lecture, we shall continue Professor Dong’s lecture to present more fundamental properties of vertex operator algebras. From the mathematical point of view, a vertex operator algebra formally resembles a Lie algebra because the Jacobi identity is used as one of the main axioms. For the Lie algebra aspect o...

Homology for Operator Algebras II : Stable Homology for Non-self-adjoint Algebras

A new homology is defined for a non-self-adjoint operator algebra with a distinguished masa which is based upon cycles and boundaries associated with complexes of partial isometries in the stable algebra. Under natural hypotheses the zeroth order group coincides with the K0 group of the generated C ∗-algebra. Several identifications and applications are given, and in particular it is shown how ...

Biflatness and Biprojectivitiy of Triangular Banach Algebras

Graded triangular algebras

Triangular Algebras and Ideals of Nest Algebras

Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...