Editing Griess algebra

{{inline |date=May 2024}}
In [[mathematics]], the '''Griess algebra''' is a [[commutative]] [[non-associative algebra]] on a [[real number|real]] [[vector space]] of [[dimension]] 196884 that has the [[Monster group]] ''M'' as its [[automorphism group]]. It is named after mathematician [[R. L. Griess]], who constructed it in 1980 and subsequently used it in 1982 to construct ''M''. The Monster fixes (vectorwise) a 1-space in this algebra and acts absolutely irreducibly on the 196883-dimensional [[orthogonal complement]] of this 1-space.
(The Monster preserves the standard [[inner product]] on the 196884-space.)

Griess's construction was later simplified by [[Jacques Tits]] and [[John H. Conway]].

The Griess algebra is the same as the degree 2 piece of the [[monster vertex algebra]], and the Griess product is one of the vertex algebra products.

==References==
*{{Citation | last1=Conway | first1=John Horton | author1-link=John Horton Conway | title=A simple construction for the Fischer-Griess monster group | doi=10.1007/BF01388521 |mr=782233 | year=1985 | journal=[[Inventiones Mathematicae]] | issn=0020-9910 | volume=79 | issue=3 | pages=513–540| bibcode=1985InMat..79..513C }}
*R. L. Griess Jr, ''The Friendly Giant'', Inventiones Mathematicae  69 (1982), 1-102

[[Category:Non-associative algebras]]
[[Category:Sporadic groups]]


{{algebra-stub}}