Given a directed graph, there exists a universal operator algebra and universal C∗-algebra associated to the directed graph. For finite graphs this algebra decomposes as the universal free product of some building block operator algebras. For countable directed graphs, the universal operator algebras arise as direct limits of operator algebras of finite subgraphs. Finally, a method for computin...

Abstract We formulate an interpretation of the theory of physical superselection sectors in terms of vertex operator algebra language. Using this formulation we give a construction of simple current from a primary semisimple element of weight one. We then prove that if a rational vertex operator algebra V has a simple current M satisfying certain conditions, then V ⊕M has a natural rational ver...

The extended W -algebra of type sl2 at positive rational level, denoted by Mp+,p− , is a vertex operator algebra that was originally proposed in [1]. This vertex operator algebra is an extension of the minimal model vertex operator algebra and plays the role of symmetry algebra for certain logarithmic conformal field theories. We give a construction ofMp+,p− in terms of screening operators and ...

The notion of vertex operator algebra ([B], [FHL], [FLM]) is the algebraic counterpart of the notion of what is now usually called “chiral algebra” in conformal field theory, and vertex operator algebra theory generalizes the theories of affine Lie algebras, the Virasoro algebra and representations (cf. [B], [DL], [FLM], [FZ]). It has been well known (cf. [FZ], [L1]) that the irreducible highes...