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Associative subalgebras of the Griess algebra. (English) Zbl 0789.17002

The authors investigate the structure of the Griess algebra \(G\), whose automorphism group is the Fisher-Griess monster \(F_ 1\). The 48- dimensional maximal associative subalgebras are constructed in \(G\), and it is conjectured that the given examples are of maximal possible dimension among all associative subalgebras in \(G\).

MSC:

17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
20C34 Representations of sporadic groups
20D08 Simple groups: sporadic groups
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