On self-similar Lie algebras and virtual endomorphisms

Author(s)

Futorny, Vyacheslav ^[1] ; Kochloukova, Dessislava H. ^[2] ; Sidki, Said N. ^[3]

Affiliation

^[1] Univ Sao Paulo, Sao Paulo - Brazil

^[2] State Univ Campinas UNICAMP, Campinas, SP - Brazil

^[3] Univ Brasilia UNB, Brasilia, DF - Brazil

• Document type: Journal article
• Source: MATHEMATISCHE ZEITSCHRIFT; v. 292, n. 3-4, p. 1123-1156, AUG 2019.
• Web of Science Citations: 0

Abstract

We introduce the notion of virtual endomorphisms of Lie algebras and use it as an approach for constructing self-similarity of Lie algebras. This is done in particular for a class of metabelian Lie algebras having homological type FPn, which are Lie algebra analogues of lamplighter groups. We establish several criteria when the existence of virtual endomorphism implies a self-similar Lie structure. Furthermore, we prove that the classical Lie algebra sln(k), where char(k) does not divide n affords non-trivial faithful self-similarity. (AU)

• FAPESP's process: 16/05271-0 - Self-similar structures and homological type FPm
• Grantee: Dessislava Hristova Kochloukova
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/05678-3 - Abstract groups, pro-p groups and Lie algebras of homological type FPm
• Grantee: Dessislava Hristova Kochloukova
• Support Opportunities: Regular Research Grants