On Griess Algebras

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2008
• ISSN: 1815-0659
• 1. Verfasser: Roitman, M.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2008
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/149024
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: On Griess Algebras / M. Roitman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 27 назв. — англ.

In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V₀ + V₂ + V₃ + ..., such that dim V₀ = 1 and V₂ contains A. We can choose V so that if A has a unit e, then 2e is t...