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arXiv · 1801.03005

On Self-Similar Lie Algebras and Virtual Endomorphisms

Vyacheslav Futorny·Dessislava H. Kochloukova·Said N. Sidki
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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.

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BibTeXRIS

Vyacheslav Futorny, Dessislava H. Kochloukova, Said N. Sidki. 2018-01-09. On Self-Similar Lie Algebras and Virtual Endomorphisms. https://arxiv.org/abs/1801.03005

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