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- Title
On self-similar Lie algebras and virtual endomorphisms.
- Authors
Futorny, Vyacheslav; Kochloukova, Dessislava H.; Sidki, Said N.
- 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 F P n , 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 s l n (k) , where char(k) does not divide n affords non-trivial faithful self-similarity.
- Publication
Mathematische Zeitschrift, 2019, Vol 292, Issue 3/4, p1123
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-018-2146-6