Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients

TL;DR

This paper thoroughly characterizes the Lie symmetries of second-order linear ODE systems with constant coefficients, providing precise bounds on their invariance algebra dimensions over real and complex fields.

Contribution

It offers a complete classification and exact bounds for the maximal Lie invariance algebras of these systems using an effective algebraic method.

Findings

Exact bounds for Lie algebra dimensions are established.

Complete classification of symmetries over real and complex fields.

Effective algebraic approach demonstrated for symmetry analysis.

Abstract

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.