Contragredient Lie algebras and Lie algebras associated with a standard pentad

Abstract

We will construct standard pentads which are analogues of Cartan subalgebras, and moreover, we will study graded Lie algebras corresponding to these standard pentads. We call such pentads pentads of Cartan type and describe them by two positive integers and three matrices. The structures of their corresponding Lie algebras are related with contragredient Lie algebras.

References in corpus (1)

• Lie algebras constructed with Lie modules and their positively and negatively graded modules

Cited by in corpus (2)

• Reduced contragredient Lie algebras and PC Lie algebras
• Graded Lie algebras and regular prehomogeneous vector spaces with one-dimensional scalar multiplication