On the Solvability of Z3-Graded Novikov Algebras

Viktor Zhelyabin; Ualbai Umirbaev

doi:10.20944/preprints202101.0438.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 20 January 2021 / Approved: 22 January 2021 / Online: 22 January 2021 (09:43:21 CET)

Let N = N₀+ N₁+ N₂ be a Z₃-graded Novikov algebra. The main goal of the paper is to prove that over a field of characteristic not equal to 3 the algebra N is solvable if N₀ is solvable. We also show that a $Z_2$-graded Novikov algebra N=N₀+ N₂ over a field of characteristic not equal to 2 is solvable if N₀ is solvable. This implies that for every n of the form n=2^k3^l, any Z_n-graded Novikov algebra N over a field of characteristic not equal to 2,3 is solvable if N₀ is solvable.

Novikov algebra; graded algebra; solvability; regular automorphism; the ring of invariants

Computer Science and Mathematics, Algebra and Number Theory

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On the Solvability of Z₃-Graded Novikov Algebras

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