On Self-Similar Lie Algebras and Virtual Endomorphisms
Rings and Algebras
2018-01-10 v1
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 Pn, which are variants of lamp-lighter 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.
Cite
@article{arxiv.1801.03005,
title = {On Self-Similar Lie Algebras and Virtual Endomorphisms},
author = {Vyacheslav Futorny and Dessislava H. Kochloukova and Said N. Sidki},
journal= {arXiv preprint arXiv:1801.03005},
year = {2018}
}