Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# On the Solvability of Z3-Graded Novikov Algebras

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

How to cite: Zhelyabin, V.; Umirbaev, U. On the Solvability of Z3-Graded Novikov Algebras. Preprints 2021, 2021010438 (doi: 10.20944/preprints202101.0438.v1). Zhelyabin, V.; Umirbaev, U. On the Solvability of Z3-Graded Novikov Algebras. Preprints 2021, 2021010438 (doi: 10.20944/preprints202101.0438.v1).

## Abstract

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=2k3l, any Zn-graded Novikov algebra N over a field of characteristic not equal to 2,3 is solvable if N0 is solvable.

## Subject Areas

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

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