The semijoin algebra is the variant of the relational algebra obtained by replacing the join operator by the semijoin operator. We provide an Ehrenfeucht-Fraissé game, characterizing the discerning power of the semijoin algebra. This game gives a method for showing that queries are not expressible in the semijoin algebra.

It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A (1) 1 of level k coincides with a certain W -algebra. In particular, a set of generators for the parafermion vertex operator algebra is determined.

The vertex operator algebras associated with positive definite even lattices afford a large family of known examples of vertex operator algebras. An isometry of the lattice induces an automorphism of the lattice vertex operator algebra. The subalgebra of fixed points of an automorphism is the so-called orbifold vertex operator algebra. In this paper we deal with the case where the lattice L = √...

A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed, left ideals in C∗-algebras may be characterized as the class of such operator algebras, which happen also to be triple systems. Conversely, we show here and in a sequel to this paper, that operator algebras with r.c.a.i. should be studied in terms of a certain le...

2 Vertex Operator Algebras 6 2.1 Notation and Conventions . . . . . . . . . . . . . . . . . . . . 6 2.2 Local Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Axioms for a Vertex Algebra . . . . . . . . . . . . . . . . . . . 9 2.4 Heisenberg Algebra . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Virasoro Algebra . . . . . . . . . . . . . . . . . . . . . . . . . 13 2....

The rational and C2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c̃ < 0 and C if c̃ = 0. If c̃ > 0, it is an extension of discrete Virasoro vertex operator algebra L(cp,q, 0) by its irreducible modules. It is also proved that for any rational and C2-cofinite sim...

The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions modeling one string propagating in space-time splitting into n strings in conformal field theory. This notion is in some sense dual to the notion of vertex operator algebra. We prove that any vertex operator algebra equipped with a non-degenerate, Virasoro preserving, bilinear form give...

We prove a generalized rationality property and a new identity that we call the “Jacobi identity” for intertwining operator algebras. Most of the main properties of genus-zero conformal field theories, including the main properties of vertex operator algebras, modules, intertwining operators, Verlinde algebras, and fusing and braiding matrices, are incorporated into this identity. Together with...

We show that the symbol of a bounded composition operator on Wiener algebra Dirichlet series does not need to belong this algebra. Our example even gives an absolutely summing (hence compact) operator.