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On solvability and nilpotency for \(n\)-Hom-Lie algebras and \((n+1)\)-Hom-Lie algebras induced by \(n\)-Hom-Lie algebras. (English) Zbl 1479.17009

Silvestrov, Sergei (ed.) et al., Algebraic structures and applications. Selected papers based on the presentations at the international conference on stochastic processes and algebraic structures – from theory towards applications, SPAS 2017, Västerås and Stockholm, Sweden, October 4–6, 2017. Cham: Springer. Springer Proc. Math. Stat. 317, 127-157 (2020).
Summary: The purpose of this work is to generalize the concepts of \(k\)-solvability and \(k\)-nilpotency, initially defined for \(n\)-Lie algebras, to \(n\)-Hom-Lie algebras and to study their properties. We define \(k\)-derived series, \(k\)-central descending series and study their properties, we show that \(k\)-solvability is a radical property and we apply all of the above to the case of \((n+1)\)-Hom-Lie algebras induced by \(n\)-Hom-Lie algebras.
For the entire collection see [Zbl 1467.16001].

MSC:

17A40 Ternary compositions
17A42 Other \(n\)-ary compositions \((n \ge 3)\)
17B30 Solvable, nilpotent (super)algebras
17B55 Homological methods in Lie (super)algebras
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