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A rational construction of Lie algebras of type E_7

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arxiv 1309.7325 v2 pith:KV6PNFGI submitted 2013-09-27 math.RA math.AG

Victor Petrov This is my paper · ORCID
classification math.RAmath.AG
keywords algebrastypeconstructionalgebrasomeadmitarisesdegree
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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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