Polynomial identities in Novikov algebras
Dotsenko V. Ismailov N. Umirbaev U.
March 2023Springer Science and Business Media Deutschland GmbH
Mathematische Zeitschrift
2023#303Issue 3
In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity satisfies some unexpected “universal” identities, in particular, right associator nilpotence, and right nilpotence of the commutator ideal. This, in particular, implies that a Novikov algebra over a field of zero characteristic satisfies a nontrivial identity if and only if it is Lie-solvable. We also establish that any system of identities of Novikov algebras over a field of zero characteristic follows from finitely many of them, and that the same holds over any field for multilinear Novikov identities. Some analogous simpler statements are also proved for commutative differential algebras.
Differential identity , Novikov algebra , Polynomial identity , Specht property
Text of the article Перейти на текст статьи
Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René-Descartes, Strasbourg CEDEX, 67000, France
Astana IT University, Astana, 010000, Kazakhstan
Department of Mathematics, Wayne State University, Detroit, 48202, MI, United States
Department of Mathematics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Institut de Recherche Mathématique Avancée
Astana IT University
Department of Mathematics
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026