D.M. Riley proved in [3] that, if A and B are either Lie nilpotent or Lie metabelian algebras, then their tensor product $A\otimes B$ is Lie soluble and obtained bounds on the Lie derived length of $A\otimes B$. The aim of the present note is to improve Riley's bounds; moreover we consider also the cases in which A and B are either strongly Lie soluble or strong Lie nilpotent algebras.
A note on the tensor product of Lie soluble algebras
CATINO, Francesco;MICCOLI, Maria Maddalena;NUCCIO, CLAUDIA
2007-01-01
Abstract
D.M. Riley proved in [3] that, if A and B are either Lie nilpotent or Lie metabelian algebras, then their tensor product $A\otimes B$ is Lie soluble and obtained bounds on the Lie derived length of $A\otimes B$. The aim of the present note is to improve Riley's bounds; moreover we consider also the cases in which A and B are either strongly Lie soluble or strong Lie nilpotent algebras.File in questo prodotto:
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