Exact solutions of Klein–Gordon equations in external electromagnetic fields on 3D de Sitter background

We study symmetry properties and the possibility of exact integration Klein–Gordon equations in external electromagnetic fields on 3D de Sitter background dS3. present an algorithm for constructing first-order algebra describe its structure terms Lie extensions. Based well-known classification subalgebras so(1,3), we classify all dS3 which corresponding admit algebras. Then, select integrable cases, each them, construct solutions using noncommutative method developed by Shapovalov Shirokov [Theor. Math. Phys. 104, 921–934 (1995)]. also propose original algebraic special local coordinates space dS3, basis vector so(1,3) have simplest form.