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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. https://doi.org/10.20944/preprints202101.0438.v1 Zhelyabin, V.; Umirbaev, U. On the Solvability of Z3-Graded Novikov Algebras. Preprints 2021, 2021010438. https://doi.org/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.
Keywords
Novikov algebra; graded algebra; solvability; regular automorphism; the ring of invariants
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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