On the classification of $3$-dimensional complex hom-Lie algebras
Abstract
We classify hom-Lie structures with nilpotent twisting map on -dimensional complex Lie algebras, up to isomorphism, and classify all degenerations in such family. The ideas and techniques presented here can be easily extrapolated to study similar problems in other algebraic structures and provide different perspectives from where one can tackle classical open problems of interest in rigid Lie algebras.
Keywords
Cite
@article{arxiv.1910.13528,
title = {On the classification of $3$-dimensional complex hom-Lie algebras},
author = {Edison Alberto Fernández-Culma and Nadina Elizabeth Rojas},
journal= {arXiv preprint arXiv:1910.13528},
year = {2019}
}
Comments
43 pages and a companion file providing a detailed, step-by-step, explanation of our results. In the previous version, we made a mistaked by affirming that the Theorem4.3 in Ongong'a, Richter, Silvestrov "Classification of 3-dim. Hom-Lie algebras" is wrong. Our error was due to that we didn't note the condition $C_{1,3}^2\neq 0$ to define the family $H_{6}^3$. Please accept our sincere apoogies