\(1+1\) -Dimensional dS (dS \(_2\) ) Relativity: The Classical Context

Dedicated to a thorough examination, this chapter provides a comprehensive review of diverse mathematical facets associated with the \(1+1\) -dimensional de Sitter (dS \(_2\) ) relativity group. The group, denoted as SO \(_0(1,2)\) or its double-covering group SU(1, 1), is meticulously explored, along with its corresponding Lie manifold and Lie algebra. Furthermore, this chapter explores the analysis of the corresponding (co-)adjoint orbits, recognizing them as inherent candidates for achieving a phase spacePhase space interpretation of classical elementary systems existing in dS \(_2\) spacetime.