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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 particleantiparticle 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.

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