Читать книгу Algebra and Applications 1 - Abdenacer Makhlouf - Страница 16

Let us assume now that F is algebraically closed and char F = 0. Kac derived the classification of finite dimensional simple Jordan F-superalgebras from his classification of simple finite dimensional Lie superalgebras via the Tits–Kantor–Koecher construction.

THEOREM 1.1 (see Kac (1977a) and Kantor (1990)).– Let be a simple Jordan superalgebra over an algebraically closed field F, char F = 0. Then J is isomorphic to one of the superalgebras in examples 1.8, 1.9 and 1.10–1.15 or it is the Kantor double of the Poisson bracket in example 1.17.

REMARK 1.3.– We will assume always in this section that .