CPT Groups of Spinor Fields in de Sitter and Anti-de Sitter Spaces

$CPT$ groups for spinor fields in de Sitter and anti-de Sitter spaces are defined in the framework of automorphism groups of Clifford algebras. It is shown that de Sitter spaces with mutually opposite signatures correspond to Clifford algebras with different algebraic structure that induces an essential difference of $CPT$ groups associated with these spaces. $CPT$ groups for charged particles are considered with respect to phase factors on the various spinor spaces related with real subalgebras of the simple Clifford algebra over the complex field (Dirac algebra). It is shown that $CPT$ groups for neutral particles which admit particle-antiparticle interchange and $CPT$ groups for truly neutral particles are described within semisimple Clifford algebras with quaternionic and real division rings, respectively. A difference between bosonic and fermionic $CPT$ groups is discussed.