Geodesic
Lie type Jordan algebras
Matematičeskie trudy, Tome 22 (2019) no. 1, pp. 127-177

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We study the variety $\mathcal{V}_J$ of Jordan algebras defined by the identities $x^2yx\equiv 0$ and $(x_1y_1)(x_2y_2)(x_3y_3)\equiv 0$. We suggest a method for constructing an algebra in $\mathcal{V}_J$ 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. 
@article{MT_2019_22_1_a5,
     author = {A. V. Popov},
     title = {Lie type {Jordan} algebras},
     journal = {Matemati\v{c}eskie trudy},
     pages = {127--177},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2019_22_1_a5/}
}
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A. V. Popov. Lie type Jordan algebras. Matematičeskie trudy, Tome 22 (2019) no. 1, pp. 127-177. http://geodesic.mathdoc.fr/item/MT_2019_22_1_a5/