{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:49:04Z","timestamp":1775465344156,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,13]],"date-time":"2021-02-13T00:00:00Z","timestamp":1613174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Program of fundamental scientific researches of the SB of RAS, project 0314-2016-0001","award":["0314-2016-0001"],"award-info":[{"award-number":["0314-2016-0001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2295N1\u2295N2 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\u2295N1 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.<\/jats:p>","DOI":"10.3390\/sym13020312","type":"journal-article","created":{"date-parts":[[2021,2,14]],"date-time":"2021-02-14T05:54:49Z","timestamp":1613282089000},"page":"312","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Solvability of \u21243-Graded Novikov Algebras"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9371-6363","authenticated-orcid":false,"given":"Viktor","family":"Zhelyabin","sequence":"first","affiliation":[{"name":"Institute of Mathematics of the SB of RAS, 630090 Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ualbai","family":"Umirbaev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, MI 48202, USA"},{"name":"Institute of Mathematics and Modeling, Almaty 050010, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,13]]},"reference":[{"key":"ref_1","first-page":"259","article-title":"Fractional powers of operators and Hamiltonian systems","volume":"10","author":"Diki","year":"1976","journal-title":"Funct. 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