Endomorphisms of Cell 2-representations

Recursive Fermion System in Cuntz Algebra . II — Endomorphism , Automorphism and Branching of Representation — Mitsuo Abe

Based on an embedding formula of the CAR algebra into the Cuntz algebra O2p , properties of the CAR algebra are studied in detail by restricting those of the Cuntz algebra. Various ∗-endomorphisms of the Cuntz algebra are explicitly constructed, and transcribed into those of the CAR algebra. In particular, a set of ∗-endomorphisms of the CAR algebra into its even subalgebra are constructed. Acc...

Classification 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...

Endomorphisms and Quantum Operations

We define a quantum operation as a special type of endomorphism between spaces of matrices. Representations of endomorphisms are considered and an isomorphism between higher dimensional matrices and endomorphisms is derived. We then employ this isomorphism to prove various results for endomorphisms and quantum operations. For example, an endomorphism is completely positive if and only if its co...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

A tensor product of representations of Cuntz algebras

We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition formulae to determine properties of endomorphisms. Mathematics Subject Classifications (2000). 47L55, 81T05.