Читать книгу Algebra and Applications 1 - Abdenacer Makhlouf - Страница 18

This case shows similarities with infinite dimensional superconformal Jordan algebras (see section 1.8) in characteristic 0.

Let us denote the algebra of truncated polynomials in m variables. Let B(m, n) = B(m) ⊗ G(n) be the tensor product of B(m) with the Grassmann algebra G(n) = 〈1, ξ₁,…, ξn〉. Then B(m, n) is an associative commutative superalgebra.

THEOREM 1.3 (Martínez and Zelmanov (2010)).– Let be a finite dimensional simple unital Jordan superalgebra over an algebraically closed field F of characteristic p > 2. If the even part is not semisimple, then there exist integers m, n and a Jordan bracket { , } on B(m, n) such that J = B(m, n) + B(m, n)v = KJ(B(m, n), { , }) is a Kantor double of B(m, n) or J is isomorphic to a Cheng–Kac Jordan superalgebra JCK(B(m), d) for some derivation d : B(m) → B(m).