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A rational construction of Lie algebras of type E_7 (1309.7325v2)
Published 27 Sep 2013 in math.RA and math.AG
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.