Group theory and generalizations Classification of finite simple groups Object
Griess algebra
Description
The Griess algebra is a real vector space of dimension with a bilinear product . The product is commutative but not associative. The algebra also carries a positive definite symmetric bilinear form that is associative: for all . Its automorphism group is the Monster group, the largest sporadic group.
Remarks
Robert Griess built this algebra to construct the Monster group, which acts on it by algebra automorphisms. As a representation of the Monster, splits as a trivial summand of dimension and an irreducible summand of dimension . The number is also the coefficient of in the expansion of the -function, a coincidence that is part of monstrous moonshine. In the moonshine module of Frenkel, Lepowsky and Meurman, a vertex operator algebra, the Griess algebra appears as the weight subspace.
Where this leads
5 pages build on this one.
Further reading
About this page
| Tag | ZMPYZ8KD9N |
|---|---|
| URI | m2://ZMPYZ8KD9N |
| Kind | object |
| Writing | W0 stub |
| MSC | 20D08, 17B69 |
| Same as | |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- an inventory row: the row of the inventory that the node accounts for (0 of 1)
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.