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We present an extremely elementary construction of the simple Lie algebrasover the complex numbers in all of their minuscule representations, using thevertices of various polytopes. The construction itself requires no complicatedcombinatorics and essentially no Lie theory other than the definition of a Liealgebra; in fact, the Lie algebras themselves appear as by-products of theconstruction.

Representations of Lie algebras arising from polytopes