More on characteristic polynomials of Lie algebras
Korkeat Korkeathikhun, Borworn Khuhirun, Songpon Sriwongsa, Keng, Wiboonton

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
