On Griess Algebras
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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2008 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2008
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149024 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Griess Algebras / M. Roitman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 27 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862592549635489792 |
|---|---|
| author | Roitman, M. |
| author_facet | Roitman, M. |
| citation_txt | On Griess Algebras / M. Roitman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.
|
| first_indexed | 2025-11-27T08:40:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149024 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T08:40:16Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Roitman, M. 2019-02-19T13:07:52Z 2019-02-19T13:07:52Z 2008 On Griess Algebras / M. Roitman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 27 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B69 https://nasplib.isofts.kiev.ua/handle/123456789/149024 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 the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple. This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Griess Algebras Article published earlier |
| spellingShingle | On Griess Algebras Roitman, M. |
| title | On Griess Algebras |
| title_full | On Griess Algebras |
| title_fullStr | On Griess Algebras |
| title_full_unstemmed | On Griess Algebras |
| title_short | On Griess Algebras |
| title_sort | on griess algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149024 |
| work_keys_str_mv | AT roitmanm ongriessalgebras |