Geodesic
Associative and Jordan Lie nilpotent algebras
Algebra i logika, Tome 62 (2023) no. 5, pp. 614-636

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We look at the interconnection between Lie nilpotent Jordan algebras and Lie nilpotent associative algebras. It is proved that a special Jordan algebra is Lie nilpotent if and only if its associative enveloping algebra is Lie nilpotent. Also it turns out that a Jordan algebra is Lie nilpotent of index $2n+1$ if and only if its algebra of multiplications is Lie nilpotent of index $2n$. Finally, we prove a product theorem for Jordan algebras.
Keywords: associative algebra, Jordan algebra, Lie nilpotent algebra, product theorem for Jordan algebras. 
@article{AL_2023_62_5_a2,
     author = {S. V. Pchelintsev},
     title = {Associative and {Jordan} {Lie} nilpotent algebras},
     journal = {Algebra i logika},
     pages = {614--636},
     publisher = {mathdoc},
     volume = {62},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_5_a2/}
}
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S. V. Pchelintsev. Associative and Jordan Lie nilpotent algebras. Algebra i logika, Tome 62 (2023) no. 5, pp. 614-636. http://geodesic.mathdoc.fr/item/AL_2023_62_5_a2/