Solvability and nilpotency of Novikov algebras. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Shestakov, Ivan; Zhang, Zerui
• Is Part Of: Communications in algebra. Volume 48:Issue 12(2020)
• Page Start: 5412
• Page End: 5420
• Publication Date: 2020-12-01
• Subjects: Solvable Novikov algebra -- automorphism -- nilpotent Novikov algebra; 08A35 -- 17A01 -- 17A30; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1789652
• Languages: English
• ISSNs: 0092-7872

Abstract

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.