Finite generation of Lie derived powers of associative algebras

2017/12/19 by Alahmadi, Adel, Alsulami, Hamed
#17B60 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1712.07303

Abstract

Let A be an associative algebra over a field of characteristic ≠ 2 that is generated by a finite collection of nilpotent elements. We prove that all Lie derived powers of A are finitely generated Lie algebras.

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• Finite generation of Lie algebras associated to associative algebras
• Associative nil-algebras over finite fields
• Finitely generated algebras with involution and their identities
• Nilpotent Lie and Leibniz algebras
• Characterizing Nilpotent Associative Algebras by Their Multiplier