More on characteristic polynomials of Lie algebras

TL;DR

This paper explores properties of characteristic polynomials of Lie algebra representations, providing new characterizations for simple and nilpotent Lie algebras based on these polynomials.

Contribution

It introduces new properties of characteristic polynomials and characterizes simple and nilpotent Lie algebras through these polynomials.

Findings

Characterization of linearization of characteristic polynomials for simple Lie algebras

Nilpotent Lie algebras characterized via characteristic polynomials of the adjoint representation

Extended understanding of properties of characteristic polynomials in Lie algebra theory

Abstract

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the linearization of characteristic polynomials. Additionally, we characterize nilpotent Lie algebras via characteristic polynomials of the adjoint representation.