(37). Quotients in graded Lie algebras. Martindale-like quotients for Kantor pairs and Lie triple systems.
Autores: E. García y M. Gómez Lozano.
Revista: Journal Algebras and Representation Theory 16 (2013) 229-238 DOI: 10.1007/s10468-011-9303-5 (JCR: 86 de 302 Factor de impacto: 0.719)
Abstract: In this paper we prove that the maximal algebra of quotients of a nondegenerate Lie algebra with a short $\mathbb{Z}$-grading is $\mathbb{Z}$-graded with the same support. As a consequence, we introduce a notion of Martindale-like quotients for Kantor pairs and Lie triple systems and construct their maximal systems of quotients.
ple Artinian rings and simple Artinian rings with involution, the description of the inner ideals of the exceptional Lie algebras (types $G_2$, $F_4$, $E_6$, $E_7$ and $E_8$) remained open. The method we use here to classify inner ideals is based on the relationship between abelian inner ideals and ${\mathbb Z}$-gradings, obtained in a recent paper of the last three named authors with E. Neher. This reduces the question to deal with root systems.