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It is shown that a certain representation of the Heisenberg type Krichever-Novikov algebra gives rise to a state field correspondence that is quite similar to the vertex algebra structure of the usual Heisenberg algebra. Finally a definition of Krichever-Novikov type vertex algebras is proposed and its relation to vertex algebras is discussed.
Let $R := R_{2}(p)=mathbb{C}[t^{pm 1}, u : u^2 = t(t-alpha_1)cdots (t-alpha_{2n})] $ be the coordinate ring of a nonsingular hyperelliptic curve and let $mathfrak{g}otimes R$ be the corresponding current Lie algebra. color{black} Here $mathfrak g$ is
We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which plays an important role in the classification of lattices. We derive a formula relating the mass f
We prove a general mirror duality theorem for a subalgebra $U$ of a simple vertex operator algebra $A$ and its coset $V=mathrm{Com}_A(U)$, under the assumption that $A$ is a semisimple $Uotimes V$-module. More specifically, we assume that $Acongbigop
We provide a ribbon tensor equivalence between the representation category of small quantum SL(2), at parameter q=exp($pi$ i/p), and the representation category of the triplet vertex operator algebra at integral parameter p>1. We provide similar quan
We introduce a subalgebra $overline F$ of the Clifford vertex superalgebra ($bc$ system) which is completely reducible as a $L^{Vir} (-2,0)$-module, $C_2$-cofinite, but it is not conformal and it is not isomorphic to the symplectic fermion algebra $m