A class of non-associative Nilpotent Jordan algebras.

The paper is devoted to study nilpotent Jordan algebras 𝒥 satisfying that 𝒥 / Ann (𝒥) is non-associative. We show that such algebras exist iff dim 𝒥 ≥ 6 and dim (𝒥 / Ann (𝒥)) ≥ 5. Also we classify, up to isomorphism, all 6 -dimensional nilpotent Jordan algebras 𝒥 such that 𝒥 / Ann (𝒥) is non-associative, over an algebraically closed field 𝔽 of characteristic ≠ 2 , 3. [ABSTRACT FROM AUTHOR]