The evolution of the spectrum of a Frobenius Lie algebra under deformation

TL;DR

This paper investigates how the spectrum of Frobenius Lie algebras can change under deformation, providing explicit examples in four and six dimensions to demonstrate spectral evolution.

Contribution

It offers the first explicit analysis of spectrum evolution in Frobenius Lie algebras under deformation, expanding understanding of their structural stability.

Findings

Spectrum of Frobenius Lie algebra can evolve under deformation

Explicit infinitesimal deformations in 4 and 6 dimensions show spectral changes

Frobenius Lie algebras are stable under deformation but their spectra are not

Abstract

The category of Frobenius Lie algebras is stable under deformation, and here we examine explicit infinitesimal deformations of four and six dimensional Frobenius Lie algebras with the goal of understanding if the spectrum of a Frobenius Lie algebra can evolve under deformation. It can.