Generalized approximately finite $W^*$-algebras

Approximately Finite Algebras

Local Characterisation of Approximately Finite Operator Algebras

We show that the family of nest algebras with r non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local characterisation of limits formed from this family. We then consider quite general regular limit algebras and characterise these algebras using a local condition w...

Remarks on Finite W Algebras

The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G ≃ so(4, 2), unitary representations of the conformal and Poincaré algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G ≃ sp(2,R) or sp(4,R ), the anyonic parameter can be se...

Translation for Finite W -algebras

A finite W -algebra U(g, e) is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element e of a complex reductive Lie algebra g. It is possible to give the tensor product of a U(g, e)-module with a finite dimensional U(g)module the structure of a U(g, e)-module; we refer to such tensor products as translati...

On the C*-envelope of approximately finite-dimensional operator algebras

The C*-envelope of the limit algebra (or limit space) of a contrac-tive regular system of digraph algebras (or digraph spaces) is shown to be an approximately finite C*-algebra and the direct system for the C*-envelope is determined explicitly.