Universal fermionization of bosons on permutative representations of the Cuntz algebra O 2
نویسنده
چکیده
Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra O2. As examples, we show fermionizations on the Fock space and the infinite wedge. Mathematics Subject Classifications (2000). 46K10, 46L60
منابع مشابه
A pr 2 00 7 Recursive boson system in the Cuntz algebra O ∞
Bosons and fermions are often written by elements of other algebras. M. Abe gave a recursive realization of the boson by formal infinite sums of the canonical generators of the Cuntz algebra O∞. We show that such formal infinite sum always makes sense on a certain dense subspace of any permutative representation of O∞. In this meaning, we can regard as if the algebra B of bosons was a unital ∗s...
متن کاملRepresentations of the Cuntz - Krieger algebras . II — Permutative representations —
We generalize permutative representations of the Cuntz algebras for the Cuntz-Krieger algebra OA for any A. We characterize cyclic permutative representations by notions of cycle and chain, and show their existence and uniqueness. We show necessary and sufficient conditions for their irreducibility and equivalence. In consequence, we have a complete classification of permutative representations...
متن کاملClassification of sectors of the Cuntz algebras by graph invariants
A unitary equivalence class of endomorphisms of a unital C∗-algebra A is called a sector of A. We introduced permutative endomorphisms of the Cuntz algebra ON in the previous work. Branching laws of permutative representations of ON by them are computed by directed regular graphs. In this article, we classify sectors associated with permutative endomorphisms of ON by their graph invariants conc...
متن کاملGeneralized permutative representations of the Cuntz algebras
We introduce representations of the Cuntz algebra ON which are parameterized by sequences in the set of unit vectors inC . These representations are natural generalization of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. We show their existence, irreducibility, equivalence, uniqueness of irreducible decomposition and decomposition formulae by using parameters of represen...
متن کاملGeneralized permutative representations of Cuntz algebras
We introduce representations of the Cuntz algebra ON which are parameterized by sequences in the set of unit vectors inC . These representations are natural generalizations of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. We show their existence, irreducibility, equivalence, uniqueness of irreducible decomposition and decomposition formulae by using parameters of represe...
متن کامل