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arXiv · 1309.7325

A rational construction of Lie algebras of type E_7

Victor Petrov
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Abstract

We give an explicit construction of Lie algebras of type $E_7$ out of a Lie algebra of type $D_6$ with some restrictions. Up to odd degree extensions, every Lie algebra of type $E_7$ arises this way. For Lie algebras that admit a $56$-dimensional representation we provide a more symmetric construction based on an observation of Manivel; the input is seven quaternion algebras subject to some relations.

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Victor Petrov. 2013-09-27. A rational construction of Lie algebras of type E_7. https://arxiv.org/abs/1309.7325

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