| Texto completo | |
| Autor(es): |
Shestakov, Ivan
;
Umirbaev, Ualbai
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Linear Algebra and its Applications; v. 734, p. 31-pg., 2026-04-01. |
| Resumo | |
We study an analogue of the Andreadakis-Johnson filtration for automorphism groups of free algebras and introduce the notion of tangent Lie algebras for certain automorphism groups, defined as subalgebras of the Lie algebra of derivations. We show that, for many classical varieties of algebras, the tangent Lie algebra is contained in the Lie algebra of derivations with constant divergence. We also introduce the concepts of approximately tame and absolutely wild automorphisms of free algebras in arbitrary varieties and employ tangent Lie algebras to investigate their properties. It is shown that nearly all known examples of wild automorphisms of free algebras are absolutely wild, with the notable exceptions of the Nagata and Anick automorphisms. We show that the Bergman automorphism of free matrix algebras of order two is absolutely wild. Furthermore, we prove that free algebras in any variety of polynilpotent Lie algebras-except for the abelian and metabelian varieties-also possess absolutely wild automorphisms. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| Processo FAPESP: | 24/14914-9 - Estrutura e representações de sistemas algébricos e suas aplicações |
| Beneficiário: | Ivan Chestakov |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 25/01683-1 - Variedades de álgebras de Lie não-matriciais |
| Beneficiário: | Ivan Chestakov |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Internacional |