Resumen de Classification of embeddings of abelian extensions of Dn into En+1
Andrew Douglas, Delaram Kahrobaei, Joe Repka
An abelian extension of the special orthogonal Lie algebra Dn is a nonsemisimple Lie algebra Dn A V, where V is a finite-dimensional representation of Dn, with the understanding that [V, V] = 0. We determine all abelian extensions of Dn that may be embedded into the exceptional Lie algebra En+1, n = 5, 6, and 7. We then classify these embeddings, up to inner automorphism. As an application, we also consider the restrictions of irreducible representations of En+1 to Dn A V, and discuss which of these restrictions are or are not indecomposable.
