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...

How many endomorphisms does a Boolean algebra have? Can we find Boolean algebras with as few endomorphisms as possible? Of course from any ultrafilter of the Boolean algebra we can define an endomorphism, and we can combine finitely many such endomorphisms in some reasonable ways. We prove that in any cardinality λ = λ0 there is a Boolean algebra with no other endomorphisms. For this we use the...

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...

Dans cet article, nous déterminons tous les couples d'endomorphismes polynomiaux permutables de degrés supérieursà 1 de C 2 qui se prolongent en des endomorphismes holomorphes de P 2 et qui possèdent deux suites d'itérés disjointes. Abstract On the commuting polynomial endomorphisms of C 2 We determine all couples of commuting polynomial endomorphisms of C 2 that extends to holomorphic endomorp...

In the study of pre-Lie algebras, concept pre-morphism arises naturally as a generalization standard notion morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative ring k with identity, and dualized in various ways to generalized morphisms (related pre-Jordan algebras) anti-pre-morphisms anti-pre-Lie algebras). We consider idempotent pre-...

Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts. We describe the structure of endomorphisms and their asymptotic lifts in some detail, and apply those results to complete the identification of asymptotic lifts of unital completely positive linear maps on von Neumann algebras in terms of t...

This paper considers the following question: Given an Anosov endomorphism f on T, whether f is topologically conjugate to some hyperbolic toral endomorphism? It is well known that the answer for Anosov diffeomorphisms and expanding endomorphisms is affirmative. However, for the remainder Anosov endomorphisms, a quite different answer is obtained in this paper, i.e., for generic Anosov endomorph...

A Quillen-Gersten type spectral sequence is drawn for the K-theory of schemes with endomorphisms. We also prove an anology of Gersten’s conjecture in the K-theory of schemes with endomorphisms for the equal characteristic case.