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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...
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Інститут математики НАН України
2008
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149024 |
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irk-123456789-1490242019-02-20T01:28:35Z On Griess Algebras Roitman, M. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149024 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Roitman, M. |
| spellingShingle |
Roitman, M. On Griess Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Roitman, M. |
| author_sort |
Roitman, M. |
| title |
On Griess Algebras |
| title_short |
On Griess Algebras |
| title_full |
On Griess Algebras |
| title_fullStr |
On Griess Algebras |
| title_full_unstemmed |
On Griess Algebras |
| title_sort |
on griess algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149024 |
| citation_txt |
On Griess Algebras / M. Roitman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 27 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT roitmanm ongriessalgebras |
| first_indexed |
2023-05-20T17:32:00Z |
| last_indexed |
2023-05-20T17:32:00Z |
| _version_ |
1796153500708634624 |