On the Solvability of Z3-Graded Novikov Algebras Full article
| Journal |
Symmetry
ISSN: 2073-8994 |
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| Output data | Year: 2021, Volume: 312, Pages: 1-13 Pages count : 13 DOI: 10.3390/sym13020312 | ||||||
| Tags | Novikov algebra; graded algebra; solvability; regular automorphism; the ring of invarian | ||||||
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Abstract:
Symmetries of algebraic systems are called automorphisms. An algebra admits an automorphism 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 = 2k3l , any Zn-graded Novikov algebra N over a field of characteristic not equal to 2, 3 is solvable if N0 is solvable.
Cite:
Zhelyabin V.
, Umirbaev U.
On the Solvability of Z3-Graded Novikov Algebras
Symmetry. 2021. V.312. P.1-13. DOI: 10.3390/sym13020312 WOS Scopus OpenAlex
On the Solvability of Z3-Graded Novikov Algebras
Symmetry. 2021. V.312. P.1-13. DOI: 10.3390/sym13020312 WOS Scopus OpenAlex
Dates:
| Submitted: | Jan 12, 2021 |
| Accepted: | Feb 9, 2021 |
| Published print: | Feb 13, 2021 |
| Published online: | Feb 13, 2021 |
Identifiers:
| Web of science: | WOS:000623142400001 |
| Scopus: | 2-s2.0-85101248251 |
| OpenAlex: | W3133203070 |