Approximately Finitely Acting Operator Algebras

1 1 M ay 2 00 0 APPROXIMATELY FINITELY ACTING OPERATOR ALGEBRAS

−→ (Ak, φk) and the operator algebras A = lim −→ (Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE = Homu(E⊗K, E⊗K) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is refer...

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...

Rational vertex operator algebras are finitely generated

It is proved that any vertex operator algebra for which the image of the Virasoro element in Zhu’s algebra is algebraic over complex numbers is finitely generated. In particular, any vertex operator algebra with a finite dimensional Zhu’s algebra is finitely generated. As a result, any rational vertex operator algebra is finitely generated. Although many well known vertex operator algebras are ...

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.

Approximately Finite Algebras