Recursive Fermion System in Cuntz Algebra . I — Embeddings of Fermion Algebra into Cuntz Algebra —

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra O2 (or O2d more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of O2 is constructed explicitly. Generalizing this construction to the case of O2p , an embedding of CAR onto the U(1)-invariant subalgebra of O2p is obtained. Restricting a permutation representation of the Cuntz algebra, we obtain the Fock representation of CAR. We apply the results to embed the algebra of parafermions of order p into O2p according to the Green’s ansatz. E-mail: [email protected] E-mail: [email protected]