Tensor products of Lie nilpotent algebras satisfying given commutator identities are proven Lie nilpotent, yielding explicit q bounds and lower bounds on codimensions in the variety N_p.
Drensky,Free Algebras and PI-Algebras: Graduate Course in Algebra, Springer, Singa- pore
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Tensor products of Lie nilpotent associative algebras and applications to codimension sequences
Tensor products of Lie nilpotent algebras satisfying given commutator identities are proven Lie nilpotent, yielding explicit q bounds and lower bounds on codimensions in the variety N_p.