On the solvability of z3-graded novikov algebras
Zhelyabin V. Umirbaev U.
February 2021MDPI AG
Symmetry
2021#13Issue 21 - 13 pp.
Symmetries of algebraic systems are called automorphisms. An algebra admits an automor-phism of finite order n if and only if it admits a Zn-grading. 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 Z2-graded Novikov algebra N = N0 ⊕ N1 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 = 2k 3l, any Zn-graded Novikov algebra N over a field of characteristic not equal to 2, 3 is solvable if N0 is solvable.
Graded algebra , Novikov algebra , Regular automorphism , Solvability , The ring of invariants
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Institute of Mathematics of the SB of RAS, Novosibirsk, 630090, Russian Federation
Department of Mathematics, Wayne State University, Detroit, 48202, MI, United States
Institute of Mathematics and Modeling, Almaty, 050010, Kazakhstan
Institute of Mathematics of the SB of RAS
Department of Mathematics
Institute of Mathematics and Modeling
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