Simplicity in the Faulkner construction
High Energy Physics - Theory
2015-05-13 v2 Rings and Algebras
Representation Theory
Abstract
We revisit the Faulkner construction of metric 3-Leibniz algebras admitting an embedding Lie (super)algebra. In the case of positive-definite signature, we relate the various notions of simplicity: of the 3-algebra, of the representation and of the embedding Lie (super)algebra. This reduces their classification to the extant classifications of simple Lie (super)algebras.
Keywords
Cite
@article{arxiv.0905.4900,
title = {Simplicity in the Faulkner construction},
author = {José Figueroa-O'Farrill},
journal= {arXiv preprint arXiv:0905.4900},
year = {2015}
}
Comments
12 pages. (v2: corrected an error in the proof of the third theorem. The results are unchanged.)