Geodesic
Frobenius Relations for Associative~Lie~Nilpotent Algebras
Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 417-422

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It is proved that any relatively free associative Lie nilpotent algebra of a class $l$ over a field of finite characteristic $p$ satisfies the additive Frobenius relation $(a+b)^{p^s}=a^{p^s}+b^{p^s}$ if and only if $l\le p^s-p^{s-1}+1$. It is also proved that, under the above conditions on the Lie class of nilpotency, the multiplicative Frobenius relation $(a\cdot b)^{p^s}=a^{p^s}\cdot b^{p^s}$ holds.
Mots-clés : Frobenius relations
Keywords: Lie nilpotent algebra. 
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     author = {S. V. Pchelintsev},
     title = {Frobenius {Relations} for {Associative~Lie~Nilpotent} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a7/}
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S. V. Pchelintsev. Frobenius Relations for Associative~Lie~Nilpotent Algebras. Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 417-422. http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a7/