Solvability and nilpotency of Novikov algebras
I. P. Shestakov, Zerui Zhang
Abstract
We first prove that a left Novikov algebra N is right nilpotent if and only if it is solvable. Then we show that, every Novikov algebra that can be represented as the sum of two solvable subalgebras is itself solvable, moreover, if the two solvable subalgebras are abelian, then the whole algebra is metabelian. Finally, we show that for every n≥2, every n-generated non-abelian free solvable (or non-abelian free right nilpotent) Novikov algebra has wild automorphisms.
Topics & Concepts
MathematicsNovikov self-consistency principleAbelian groupNilpotentNilpotent groupPure mathematicsAlgebra over a fieldSolvable groupAdvanced Topics in AlgebraRings, Modules, and AlgebrasAlgebraic structures and combinatorial models