2012/10/26 by Thomas J. Robinson, Robinson, Thomas J.
Mathematics · Physics and Astronomy · #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1210.7148
openalex publication_date 2012/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.