I understand Lie groups are defined by the structure constants associated with the lie brackets, which are treated as commutators in quantum mechanics, but i dont know of a math theory related to group theory to define or use an anti commutator. If Lie groups theory uses the commutator, what theory uses the anti commutator?
Finite groups (not Lie groups, which are continuous), can be specified by structure equations analogous to a Lie bracket, but more general, of which commutation or anti commutation relations are just one of infinite possibilities. Is there such variety of possible structure equations in continuous groups too?