A rational construction of Lie algebras of type E_7
Rings and Algebras
2015-07-06 v2 Algebraic Geometry
Abstract
We give an explicit construction of Lie algebras of type out of a Lie algebra of type with some restrictions. Up to odd degree extensions, every Lie algebra of type arises this way. For Lie algebras that admit a -dimensional representation we provide a more symmetric construction based on an observation of Manivel; the input is seven quaternion algebras subject to some relations.
Keywords
Cite
@article{arxiv.1309.7325,
title = {A rational construction of Lie algebras of type E_7},
author = {Victor Petrov},
journal= {arXiv preprint arXiv:1309.7325},
year = {2015}
}
Comments
New version contains 7A_1-construction; the proof of Theorem 3 has been simplified