An Effective Criterion for Nielsen-Schreier Varieties
Dotsenko V. Umirbaev U.
1 December 2023Oxford University Press
International Mathematics Research Notices
2023#2023Issue 2320385 - 20432 pp.
To the memory of V. A. Artamonov (1946-2021) All algebras of a certain type are said to form a Nielsen-Schreier variety if every subalgebra of a free algebra is free. This property has been perceived as extremely rare; in particular, only six Nielsen-Schreier varieties of algebras with one binary operation have been discovered in prior work on this topic. We propose an effective combinatorial criterion for the Nielsen-Schreier property in the case of algebras over a field of zero characteristic; in our approach, operads play a crucial role. Using this criterion, we show that the well-known varieties of all pre-Lie algebras and of all Lie-admissible algebras are Nielsen-Schreier, and, quite surprisingly, that there are already infinitely many non-equivalent Nielsen-Schreier varieties of algebras with one binary operation and identities of degree four.
Text of the article Перейти на текст статьи
Institut de Recherche Mathematique Avancee, Umr 7501, Universite de Strasbourg et Cnrs, 7 rue Rene-Descartes CEDEX, Strasbourg, 67000, France
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 Mathematique Avancee
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