📖 Anti Jordan Pairs. Automorphisms Of Simple 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.