Lie nilpotent Novikov algebras and Lie solvable Leavitt path algebras

2020/12/21 by Zhang, Zerui, Nam, Tran Giang
#16S88 #17A01 #17A30 #17B30 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2012.11191

Abstract

In this paper, we first study properties of the lower central chains for Novikov algebras. Then we show that for every Lie nilpotent Novikov algebra~N, the ideal of~N generated by the set~\ab - ba| a, b∈ N\ is nilpotent. We secondly provide necessary and sufficient conditions on the graph E and the field K for which the Leavitt path algebra L_K(E) is Lie solvable. Consequently, we obtain a complete description of Lie nilpotent Leavitt path algebras, and show that the Lie solvability of~L_K(E) and the Lie nilpotency of [L_K(E),L_K(E)] are the same.

Related

• On the Lie-solvability of Novikov algebras
• Novikov algebras and Novikov structures on Lie algebras
• A Talented Monoid View on Lie Bracket Algebras over Leavitt Path Algebras
• Polynomial identities in Novikov algebras
• Leavitt path algebras in which every Lie ideal is an ideal and applications