Sur les endomorphismes holomorphes permutables de $$\mathbb{P}^k$$

Let , be holomorphic endomorphisms of of degrees , . Assume that and that for all integers , . We then show that are critically finite. Moreover there is an orbifold such that , are coverings of . In the case we give the list of commuting pairs satisfying the above conditions. We also show that any endomorphism is approximable by endomorphisms commuting only with their iterates.

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Sur les endomorphismes holomorphes permutables de $\mathbb{P}^k$

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Received: 6 April 2001 / Published online: 17 June 2002     

PIECEWISE ENDOMORPHISMS OF RING MODULES

Abstract

We study centralizer near-rings of ring modules which are rather special in two respects. Firstly, the elements of the near-rings are piecewise endomorphisms of the modules concerned. and secondly, the near-rings themselves are, in fact, rings.     

Quasicompact and Riesz endomorphisms of Banach algebras

Let B be a unital commutative semi-simple Banach algebra. We study endomorphisms of B which are also quasicompact operators or Riesz operators. Clearly compact and power compact endomorphisms are Riesz and hence quasicompact. Several general theorems about quasicompact endomorphisms are proved, and these results are then applied to the question of when quasicompact or Riesz endomorphisms of certain algebras are necessarily power compact.     

The Anosov Relation for Nielsen Numbers of Maps of Infra-Nilmanifolds

The relative ranks of the monoid of endomorphisms of a strong independence algebra of infinite rank modulo two distinguished subsets are calculated. These subsets are the group of automorphisms and the endomorphisms α satisfying α² = α. The extra generators are characterised in each case.     

Calculating the Number of Functions with a Given Endomorphism

An iterative procedure is proposed for calculating the number of k-valued functions of n variables such that each one has an endomorphism different from any constant and permutation. Based on this procedure, formulas are found for the number of three-valued functions of n variables such that each one has nontrivial endomorphisms. For any arbitrary semigroup of endomorphisms, the power is found of the set of all three-valued functions of n variables such that each one has endomorphisms from a specified semigroup.     

A very rigid Boolean algebra

A Boolean algebra is constructed having only those endomorphisms corresponding to prime ideals, which are present in any BA. The BA constructed is of powerc, has 2 ^c endomorphisms, and is not rigid in Bonnet’s sense.     

On finite critical lattices

Critical lattices are considered, i.e., lattices without nontrivial endomorphisms and not containing nontrivial proper sublattices without nontrivial endomorphisms. It is proved that there exist n-element critical sublattices for any n ≥ 21.     

A generalization of de Bruijn graphs and classification of endomorphisms of Cuntz algebras by graph invariants

The classification problem of endomorphisms of the Cuntz algebra O_N\mathcal{O}_{N} is solved by using graph theory. We introduce permutative de Bruijn graphs as generalizations of de Bruijn graphs. Branching laws for a permutative endomorphism ρ of O_N\mathcal{O}_{N} are computed by using the permutative de Bruijn graph associated with ρ. According to this correspondence between endomorphisms and graphs, we classify permutative endomorphisms of O_N\mathcal{O}_{N} by graph invariants concretely.     

Graded Endomorphism Rings and Equivalences

Abstract

Let R be a G-graded ring,M a G-graded Σ-quasiprojective R- module,and E = END _R (M) its graded ring of endomorphisms. For any subgroup H of G,we prove that certain full subcategories of G/H-graded R-modules associated with M are equivalent to a quotient category of G/H-graded E-modules determined by the idempotent G-graded ideal of E consisting of endomorphisms which factor through a finitely generated submodule of M. Properties and applications of these equivalences are also examined.     

Split graphs whose half-strong endomorphisms form a monoid

In this paper,the half-strong,the locally strong and the quasi-strong endomorphisms of a split graph are investigated.Let X be a split graph and let End(X),hEnd(X),lEnd(X) and qEnd(X) be the endomorphism monoid,the set of all half-strong endomorphisms,the set of all locally strong endomorphisms and the set of all quasi-strong endomorphisms of X,respectively.The conditions under which hEnd(X) forms a submonoid of End(X) are given.It is shown that lEnd(X) = qEnd(X) for any split graph X.The conditions under which lEnd(X)(resp.qEnd(X)) forms a submonoid of End(X) are also given.In particular,if hEnd(X) forms a monoid,then lEnd(X)(resp.qEnd(X)) forms a monoid too.     

A note on cocycle-conjugate endomorphisms of von Neumann algebras

We show that two cocycle-conjugate endomorphisms of an arbitrary von Neumann algebra that satisfy certain stability conditions are conjugate endomorphisms, when restricted to some specific von Neumann subalgebras. As a consequence of this result, we obtain a new criterion for conjugacy of Powers shift endomorphisms acting on factors of type

     

Pseudocharacters on free groups, invariant with respect to some types of endomorphisms

We investigate methods for constructing nontrivial pseudocharacters on a free group F _n invariant with respect to certain types of endomorphisms. We find some conditions for endomorphisms of the free group under which there is a nontrivial pseudocharacter that is invariant with respect to these endomorphisms. We consider free products $ R = \tilde{R}*\prod\limits_{{i = k}}^n {\left\langle {{r_i}} \right\rangle } $ , where one factor is F _n , and the other factor is a group on which there is a pseudocharacter. For such products we obtain a similar result about the conditions of existence of nontrivial pseudocharacters invariant with respect to certain endomorphisms.     

Limit Automorphisms of the <Emphasis Type="Italic">C</Emphasis>*-Algebras Generated by Isometric Representations for Semigroups of Rationals

We consider inductive sequences of Toeplitz algebras whose connecting homomorphisms are defined by collections of primes. The inductive limits of these sequences are C*-algebras generated by representations for semigroups of rationals. We study the limit endomorphisms of these C*-algebras induced by morphisms between copies of the same inductive sequences of Toeplitz algebras. We establish necessary and sufficient conditions for these endomorphisms to be automorphisms of the algebras.     

Locally strong endomorphisms of paths

We determine the number of locally strong endomorphisms of directed and undirected paths—direction here is in the sense of a bipartite graph from one partition set to the other. This is done by the investigation of congruence classes, leading to the concept of a complete folding, which is used to characterize locally strong endomorphisms of paths. A congruence belongs to a locally strong endomorphism if and only if the number l of congruence classes divides the length of the original path and the points of the path are folded completely into the l classes, starting from 0 to l and then back to 0, then again back to l and so on. It turns out that for paths locally strong endomorphisms form a monoid if and only if the length of the path is prime or equal to 4 in the undirected case and in the directed case also if the length is 8. Finally some algebraic properties of these monoids are described.     

Lifting endomorphisms to automorphisms

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 their minimal dilations to endomorphisms.

     

Localization with Respect to Endomorphisms

Abstract. We introduce the class of localizable monoids. It contains inverse monoids. Then we define localizations of monoids with respect to localizable submonoids of their monoid of endomorphisms. These constructions can be applied to a category of left modules or to a category of A -rings. As a result, we are able to invert endomorphisms within the original category, unlike inversive localizations of Cohn's type which need a base change.