KN Superalgebras with Vertex Operators

Local Systems of Vertex Operators, Vertex Superalgebras and Modules

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operat...

Local Systems of Twisted Vertex Operators, Vertex Operator Superalgebras and Twisted Modules

We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superal...

On the Defining Number of (2n - 2)-Vertex Colorings of Kn x Kn

A supergeometric interpretation of vertex operator superalgebras

Conformal field theory (or more specifically, string theory) and related theories (cf. [BPZ], [FS], [V], and [S]) are the most promising attempts at developing a physical theory that combines all fundamental interactions of particles, including gravity. The geometry of this theory extends the use of Feynman diagrams, describing the interactions of point particles whose propagation in time sweep...

Cohomological Operators and Covariant Quantum Superalgebras

We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GLqp(1|1). In particular, we show that a unique quantum superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GLqp(1|1), is exactly identical to that obeyed by t...