Contragredient Lie algebras and Lie algebras associated with a standard pentad

2016/04/08 by Nagatoshi Sasano, Sasano, Nagatoshi · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1604.02225

openalex publication_date 2016/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

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

Related

• A class of Lie algebras who contains a class of Kac-Moody algebras
• Lie algebras constructed with Lie modules and their positively and negatively graded modules
• Contragredient Lie algebras in symmetric categories
• Reduced contragredient Lie algebras and PC Lie algebras
• Cartanification of contragredient Lie superalgebras