Generalized Clifford algebras

We consider generalized Clifford algebras with a special commutation rule that depend on a primitive root from identity. In these algebras a main set of (noncommutative) generators is completed with a set of commutative generators. In more details we consider generalized Clifford algebras of second order. In particular, we discuss an operator of Hermitian conjugation of elements of generalized Clifford algebras.