Reduced contragredient Lie algebras and PC Lie algebras

2016/07/26 by Nagatoshi Sasano, Sasano, Nagatoshi · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1607.07546

openalex publication_date 2016/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The first aim of this paper is to show that any finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation can be embedded into some PC Lie algebra. The second aim is to find the structure of a PC Lie algebra.

Citations

• Lie algebras constructed with Lie modules and their positively and negatively graded modules
• Contragredient Lie algebras and Lie algebras associated with a standard pentad

Cited by

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

Related

• Minimal faithful representations of reductive Lie algebras
• A class of Lie algebras who contains a class of Kac-Moody algebras
• Contragredient Lie algebras and Lie algebras associated with a standard pentad
• Graded Lie algebras and regular prehomogeneous vector spaces with one-dimensional scalar multiplication
• The index of centralizers of elements of reductive Lie algebras