The Existence of Superinvolutions

Elduque, Alberto and Villa, Oliver (2008) The Existence of Superinvolutions. Journal of Algebra, 319 (10). pp. 4338-4359. ISSN 0021-8693

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Superinvolutions on graded associative algebras constitute a source of Lie and Jordan superalgebras. Graded versions of the classical Albert and Albert–Riehm Theorems on the existence of superinvolutions are proven. Surprisingly, the existence of superinvolutions of the first kind is a rare phenomenon, as nontrivial central division superalgebras are never endowed with this kind of superinvolutions.

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