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arXiv · 1210.7148

Embedding of certain vertex algebras without vacuum into vertex algebras

Thomas J. Robinson
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Abstract

We show that certain vertex algebras without vacuum vector may be embedded into vertex algebras. The result is a partial analogue of the simple classical fact that any rng can be embedded into a ring. A one-line proof of the case of a vacuum-free vertex algebra (whose vertex operator map is by definition injective) appeared in Robinson (2010) using a powerful result from the representation theory of vertex algebras as algebras of mutually local weak vertex operators. Here we present a more elementary proof of a somewhat more general case. We also show that our constructions are canonical.

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Thomas J. Robinson. 2012-10-26. Embedding of certain vertex algebras without vacuum into vertex algebras. https://arxiv.org/abs/1210.7148

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