PostLie algebra structures on the Lie algebra sl(2,C)
Rings and Algebras
2013-02-05 v1 Quantum Algebra
Abstract
The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and integrable systems. We give a complete classification of PostLie algebra structures on the Lie algebra sl(2,C) up to isomorphism. We first reduce the classification problem to solving an equation of 3 x 3 matrices. To solve the latter problem, we make use of the classification of complex symmetric matrices up to the congruent action of orthogonal groups.
Cite
@article{arxiv.1111.6128,
title = {PostLie algebra structures on the Lie algebra sl(2,C)},
author = {Yu Pan and Qing Liu and Chengming Bai and Li Guo},
journal= {arXiv preprint arXiv:1111.6128},
year = {2013}
}
Comments
20 pages