Anti Jordan Pairs

Anti-Jordan pairs were introduced by Faulkner and Ferrar. Faulkner and Ferrar classified the finite dimensional simple anti-Jordan pairs over an algebraically closed field F of characteristic zero, using methods from Lie superalgebra theory in 1980. First We describe the automorphism groups and involutions of the rectangular matrix pair, the symmetric-skew pair and the symplectic anti-Jordan pair. Then we use this to classify finite dimensional simple anti-Jordan triple systems over an algebraically closed field of characteristic zero,because anti-Jordan triple systems are isomorphic to anti-Jordan pairs with involution.

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I was born in 1972. I am married and have two kids. I got my PhD degree in Mathematics in 2008. My field of research is Semigroups and Lie algebras related to nonassociative structures like anti-Jordan pairs. My profession is teaching.