Compact ideals and rigidity of representations for amenable operator algebras

Boundary Representations for Operator Algebras

All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C-envelope.

Irreducible Representations of Operator Algebras

Representations of vertex operator algebras

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69

Compact representations of BL-algebras

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local

Amenable Representations and Finite Injective Von Neumann Algebras

Let U(M) be the unitary group of a finite, injective von Neumann algebra M . We observe that any subrepresentation of a group representation into U(M) is amenable in the sense of Bekka; this yields short proofs of two known results—one by Robertson, one by Haagerup—concerning group representations into U(M). A unitary representation π of a group Γ on a Hilbert space Hπ is amenable if there exis...