We study the variety ν_J of Jordan algebras defined by the identities x²yx ≡ 0 and (x₁y₁)(x₂y₂)(x₃y₃) = 0. We suggest a method for constructing an algebra in ν_J from an arbitrary Lie superalgebra. For certain subvarieties, we completely describe their identities and sequences of cocharacters. As a corollary, we obtain the first example of a variety of Jordan algebras with fractional exponential growth.

中文翻译：

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李型约旦代数

我们研究了各种ν _Ĵ约旦代数恒等式所定义X ² YX ≡0和（X _1个Ý ₁）（X ₂ Ý ₂）（X ₃ Ý ₃）= 0。我们建议的方法用于在构建代数ν任意李李超代数的_J。对于某些子变体，我们完整地描述了它们的同一性和共性序列。作为推论，我们获得了具有分数指数增长的各种约旦代数的第一个例子。