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arXiv · 1605.06259

Minimal linear representations of filiform Lie algebras and their application for construction of Leibniz algebras

I. A. Karimjanov·M. Ladra
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Abstract

In this paper we find minimal faithful representations of several classes filiform Lie algebras by means of strictly upper-triangular matrices. We investigate Leibniz algebras whose corresponding Lie algebras are filiform Lie algebras such that the action $I \times L \to I$ gives rise to a minimal faithful representation of a filiform Lie algebra. The classification up to isomorphism of such Leibniz algebras is given for low-dimensional cases.

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I. A. Karimjanov, M. Ladra. 2016-05-20. Minimal linear representations of filiform Lie algebras and their application for construction of Leibniz algebras. https://arxiv.org/abs/1605.06259

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