Generalized Vertex Algebras and Relative Vertex Operators

Vertex Algebras and Algebraic Curves

“…We start in §2 with the axiomatic definition of vertex algebra, which is somewhat different from, but equivalent to Borcherds' 875-02 original definition (see [DL,FKRW,K2]). We then discuss some of their most important properties and give the first examples, which come from infinite-dimensional Lie algebras, such as Heisenberg, affine Kac-Moody and the Virasoro algebra.…”

Self-dual codes over the Kleinian four group

“…the set of irreducible V -modules form an abelian group G under the fusion product (cf. [DL93]). The map α : G −→ C * , M → e 2πih(M) , where h(M ) is the conformal weight of the V -module M defines a quadratic form on G and can be interpreted as an element of H 4 (K(G, 2), C * ); where K(G, 2) is the Eilenberg-MacLane space with π 2 (K(G, 2)) ∼ = G (see [Höhb]).…”

Realizations of Affine Lie Algebra $${A^{(1)}_1}$$ at Negative Levels

“…Representations of the affine Lie algebras at other levels also have attracted a lot of attention [17,14,7,5,6]. Wakimoto [20] derived a general scheme to realize the affine Lie algebra of type A (1) 1 and this was generalized to higher rank by Feigin and E. Frenkel [8].…”

“…In the monograph [5], Dong and Lepowsky constructed canonical generalized vertex operator algebras for g (of simply laced typesÂ,D orÊ) and pointed out that the corresponding quotient space for the vacuum space of any positive integer level k standardĜ-module is a module of the generalized vertex operator algebra. Furthermore, as an illustration, they showed in details the construction for A (1) 1 .…”