Linear and nonlinear representations of Galilei groups in two-dimensional space-time

Abstract

We study Galilei groups represented as groups of Lie transformations in the space of two independent variables and one dependent variable. We classify the representations of the groups A G ₁(1,1), A G ₂(1,1), A G ₃(1,1), A ~G ₁ (1,1), A ~G ₂ (1,1), and A ~G₃(1,1) in the class of Lie vector fields.