Mathematica Eterna
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The Killing Forms of Symplectic Ternary Algebras

BAI Ximei and Bai Ruipu

Symplectic ternary algebras are introduced in connection with Lie triple systems. The authors obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and investigate the relationship among the Killing forms of a real Symplectic Ternary Algebras U0, the complexification U, and the realification UR of U.