Vertex algebras generated by Lie algebras

Details Vertex algebras generated by Lie algebras Vertex algebras generated by Lie algebras

1999-01-22

arxiv.org/abs/math/9901095v1

Mathematics

Quantum Algebra

38 pages, LaTeX

Scientific paper

In this paper we introduce a notion of vertex Lie algebra U, in a way a "half" of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a subset of V(U) which generates V(U) and that the vertex Lie algebra structure on U is induced by the vertex algebra structure on V(U). Moreover, for any vertex algebra V a given homomorphism from U to V of vertex Lie algebras extends uniquely to a homomorphism from V(U) to V of vertex algebras. In the second part of paper we study under what conditions on structure constants one can construct a vertex Lie algebra U by starting with a given commutator formula for fields.

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