The existence of superinvolutions |
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| Authors: | A Elduque O Villa |
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| Institution: | 1. Departamento de Matemáticas e Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain;2. Departamento de Matemáticas, Universidad de Zaragoza, Pza. San Francisco s/n, 50009 Zaragoza, Spain |
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| Abstract: | 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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