Lie symmetries of systems of second-order linear ordinary differential   equations with constant coefficients
  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. 
Vyacheslav M. Boyko, Roman O. Popovych and Nataliya M. Shapoval
math.CA math-ph math.MP