Semigroups of matrices of intermediate growth

Autor:	Cedó, Ferran, Okniski, Jan, Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
Rok vydání:	2021
Předmět:	Mathematics::Operator Algebras Semigrups Matrius (Matemàtica)
Zdroj:	Recercat. Dipósit de la Recerca de Catalunya instname Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona
Popis:	Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This 'growth alternative' conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::1a1593679f0daca368d83e8c73d2a501 http://hdl.handle.net/2072/418877 Zobrazit plný text záznamu