  Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are
studied. For models with constant non-Abelian gauge potentials and extended
parity inversions compact and noncompact Lie group components are analyzed via
Cartan decompositions. A Lie triple structure is found and an interpretation as
PT-symmetrically generalized Jaynes-Cummings model is possible with close
relation to recently studied cavity QED setups with transmon states in
multilevel artificial atoms. For models with Abelian gauge potentials a hidden
Clifford algebra structure is found and used to obtain the fundamental symmetry
of Krein space related J-selfadjoint extensions for PTQM setups with
ultra-localized potentials.
