The existence of superinvolutions

Details The existence of superinvolutions The existence of superinvolutions

2007-04-24

arxiv.org/abs/0704.3127v1

Mathematics

Rings and Algebras

21 pages

Scientific paper

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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