837 research outputs found
Finite vertex algebras and nilpotence
I show that simple finite vertex algebras are commutative, and that the Lie
conformal algebra structure underlying a reduced (i.e., without nilpotent
elements) finite vertex algebra is nilpotent.Comment: 24 page
A remark on simplicity of vertex algebras and Lie conformal algebras
I give a short proof of the following algebraic statement: if a vertex
algebra is simple, then its underlying Lie conformal algebra is either abelian,
or it is an irreducible central extension of a simple Lie conformal algebra.Comment: 6 pages. Some typos corrected. Removed a wrongly stated associativity
propert
Bosonizations of and Integrable Hierarchies
We construct embeddings of in lattice vertex
algebras by composing the Wakimoto realization with the
Friedan-Martinec-Shenker bosonization. The Kac-Wakimoto hierarchy then gives
rise to two new hierarchies of integrable, non-autonomous, non-linear partial
differential equations. A new feature of our construction is that it works for
any value of the central element of ; that is, the
level becomes a parameter in the equations
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