An effective criterion for Nielsen-Schreier varieties

Autor:	Dotsenko, Vladimir, Umirbaev, Ualbai
Rok vydání:	2022
Předmět:	Mathematics - Rings and Algebras Mathematics - Category Theory Mathematics - K-Theory and Homology 17A50 (Primary) 08B20 16S10 18M70 18M80 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 35 pages, to appear in IMRN
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.05364 Zobrazit plný text záznamu View this record from Arxiv