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In mathematics, the Griess algebra is a commutative non-associative algebra on a 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== * *R. L. Griess, Jr, ''The Friendly Giant'', Inventiones Mathematicae 69 (1982), 1-102 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Griess algebra」の詳細全文を読む スポンサード リンク
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