The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures meromorphically induced by conformal equivalence classes of worldsheets. We then show this category is isomorphic to the category of vertex operator coalgebras...

A conformal vector with central charge c in a vertex operator algebra is an element of weight two whose component operators satisfy the Virasoro algebra relation with central charge c. Then the vertex operator subalgebra generated by the vector is isomorphic to a highest weight module for the Virasoro algebra with central charge c and highest weight 0 (cf. [M]). Let V2Al be the vertex operator ...

We perform a systematic investigation of free-scalar realisations of the Zamolodchikov W 3 algebra in which the operator product of two spin-three generators contains a non-zero operator of spin four which has vanishing norm. This generalises earlier work where such an operator was required to be absent. By allowing this spin-four null operator we obtain several realisations of the W 3 algebra ...

In a previous study [Li3], the physical super selection principle in vertex operator algebra theory seems to tell us that for a vertex operator algebra V , one should be able to obtain each irreducible V -module from the adjoint module V by changing certain things. To a certain extent, what we are expecting is an analogue of the orbital construction of representations for a Lie group [Ki]. This...

We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a by-product we obtain results about the Frobenius--Schur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity. We...

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

In this paper, we investigate, for a locally compact groupG, the operator amenability of the Fourier-Stieltjes algebra B(G) and of the reduced Fourier-Stieltjes algebra Br(G). The natural conjecture is that any of these algebras is operator amenable if and only if G is compact. We partially prove this conjecture with mere operator amenability replaced by operator C-amenability for some constant...

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1 2 , two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1 ...

It is known that the generator of a strictly continuous one parameter unitary group in the multiplier algebra of a C∗ -algebra is affiliated to that C∗ -algebra . We show that under natural non degeneracy conditions, this self adjoint unbounded operator lies indeed in the (unbounded) multiplier algebra of the Pedersen’s ideal of the C∗ -algebra .

One of the most important auxiliary objects associated with an operator algebra is its state space. The two books under review describe the authors’ solutions, obtained together with H. Hanche-Olsen and B. Iochum [1], [2], [9], to the problems: What data must be added to a state space so that the operator algebra can be recovered? and Which convex sets can arise as state spaces? As that work is...