Classification of embeddings of abelian extensions of Dn into En+1
- Autores: Andrew Douglas, Delaram Kahrobaei, Joe Repka
- Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 217, Nº 10, 2013, págs. 1942-1954
- Idioma: inglés
- DOI: 10.1016/j.jpaa.2013.01.010
- Enlaces
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Resumen
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.
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