Semigroup Of Endomorphisms Research Articles

Automorphisms of the category of free dimonoids

We prove that every automorphism of the category of free finitely generated dimonoids is quasi-inner. Also we show the automorphism group of the endomorphism semigroup of the free dimonoid on a nonsingleton set is isomorphic to the direct product of the Klein four-group and the symmetric group.

A Tits alternative for endomorphisms of the projective line

We prove an analog of the Tits alternative for endomorphisms of \mathbb{P}^1 . In particular, we show that if S is a finitely generated semigroup of endomorphisms of \mathbb{P}^1 over \mathbb{C} , then either S has polynomially bounded growth or S contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field of any characteristic and \operatorname{Prep}(f) \not= \operatorname{Prep}(g) , then for all sufficiently large j , the semigroup \langle f^j, g^j \rangle is a free semigroup on two generators.

On the semigroup of injective monoid endomorphisms of the monoid B_ω^F^3 with a three element family F^3 of inductive nonempty subsets of ω

On the semigroup of injective monoid endomorphisms of the monoid B_ω^F^3 with a three element family F^3 of inductive nonempty subsets of ω

On the semigroup of non-injective monoid endomorphisms of the semigroup B_ω^F with the two-element family F of inductive nonempty subsets of ω

On the semigroup of non-injective monoid endomorphisms of the semigroup B_ω^F with the two-element family F of inductive nonempty subsets of ω

The semigroup of endomorphisms with restricted range of an independence algebra

Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence algebras, a natural question that arises is whether by taking the semigroup T(mathscr {A}, mathscr {B}) of all endomorphisms of an independence algebra mathscr {A} whose image lie in a subalgebra mathscr {B} , one can obtain corresponding results as in the cases of sets and vector spaces. In this paper, we put under a common framework the research from Sanwong, Sommanee, Sullivan, Mendes-Gonçalves and all their predecessors. We describe Green’s relations as well as the ideals of T(mathscr {A}, mathscr {B}) following their lead. We then take a new direction, completely describing all of the extended Green’s relations on T(mathscr {A}, mathscr {B}) . We make no restriction on the dimension of our algebras as the results in the finite and infinite dimensional cases generally take the same form.

Extensions of semigroups by the dihedral groups and semigroup C∗-algebras

We consider the semidirect product [Formula: see text] of the additive group [Formula: see text] of all integers and the multiplicative semigroup [Formula: see text] of integers without zero relative to a semigroup homomorphism [Formula: see text] from [Formula: see text] to the endomorphism semigroup of [Formula: see text]. It is shown that this semidirect product is a normal extension of the semigroup [Formula: see text] by the dihedral group, where [Formula: see text] is the multiplicative semigroup of all natural numbers. Further, we study the structure of [Formula: see text]-algebras associated with this extension. In particular, we prove that the reduced semigroup [Formula: see text]-algebra of the semigroup [Formula: see text] is topologically graded over the dihedral group. As a consequence, there exists a structure of a free Banach module over the reduced semigroup [Formula: see text]-algebra of [Formula: see text] in the underlying Banach space of the reduced semigroup [Formula: see text]-algebra of [Formula: see text].

ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS

In this article, we explore the automorphisms of endomorphism semigroups and automorphism groups of the finite elementary Abelian groups. In particular, we prove that $\mathrm{Aut}(\mathrm{End}(\Z_p\oplus\Z_p\oplus\cdots\oplus\Z_p))$ can be canonically embedded into $\mathrm{Aut}(\mathrm{Aut}(\Z_p\oplus\Z_p\oplus\cdots\oplus\Z_p))$ using an elementary approach based on matrix operations. We also show that all automorphisms of $\mathrm{End}(\Z_p\oplus\Z_p\oplus\cdots\oplus\Z_p)$ are inner.

On the semigroup of injective endomorphisms of the semigroup $\mathbf{B}_\omega^{\it F_n}$ which is generated by the family $\it F_n$ of initial finite intervals of $\omega$

On the semigroup of injective endomorphisms of the semigroup $\mathbf{B}_\omega^{\it F_n}$ which is generated by the family $\it F_n$ of initial finite intervals of $\omega$

On the semigroup of injective monoid endomorphisms of the monoid B_ω^F with the two-elements family F of inductive nonempty subsets of ω

On the semigroup of injective monoid endomorphisms of the monoid B_ω^F with the two-elements family F of inductive nonempty subsets of ω

On a Class of Quotient Divisible Abelian Groups with Isomorphic Endomorphism Semigroups

On a Class of Quotient Divisible Abelian Groups with Isomorphic Endomorphism Semigroups

A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

Motivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in {mathbb {R}}^{n} and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than {mathbb {Z}}^{*}={mathbb {Z}}{setminus }{0}) semigroup of conformal endomorphisms (the analogs of isogenies for abelian varieties). We then exhibit several geometric constructions of tori with this property and study the class of conformally equivalent lattices in order to describe the moduli space of the corresponding tori.

CLASSIFICATION OF 3-GRADED CAUSAL SUBALGEBRAS OF REAL SIMPLE LIE ALGEBRAS

Let ( mathfrak{g} , τ) be a real simple symmetric Lie algebra and let W ⊂ mathfrak{g} be an invariant closed convex cone which is pointed and generating with τ(W) = −W. For elements h ∈ mathfrak{g} with τ(h) = h, we classify the Lie algebras mathfrak{g} (W, τ, h) which are generated by the closed convex cones {C}_{pm}left(W,tau, hright):= left(pm Wright)cap {mathfrak{g}}_{pm 1}^{-tau }(h) , where {mathfrak{g}}_{pm 1}^{-tau }(h):= left{xin mathfrak{g}:tau (x)=-xleft[h,xright]=pm xright} . These cones occur naturally as the skew-symmetric parts of the Lie wedges of endomorphism semigroups of certain standard subspaces. We prove in particular that, if mathfrak{g} (W, τ, h) is non-trivial, then it is either a hermitian simple Lie algebra of tube type or a direct sum of two Lie algebras of this type. Moreover, we give for each hermitian simple Lie algebra and each equivalence class of involutive automorphisms τ of mathfrak{g} with τ(W) = −W a list of possible subalgebras mathfrak{g} (W, τ, h) up to isomorphy.

Covariants, Invariant Subsets, and First Integrals

Let $k$ be an algebraically closed field of characteristic 0, and let $V$ be a finite-dimensional vector space. Let $End(V)$ be the semigroup of all polynomial endomorphisms of $V$. Let $E$ be a subset of $End(V)$ which is a linear subspace and also a semi-subgroup. Both $End(V)$ and $E$ are ind-varieties which act on $V$ in the obvious way. In this paper, we study important aspects of such actions. We assign to $E$ a linear subspace $D_{E}$ of the vector fields on $V$. A subvariety $X$ of $V$ is said to $D_{E}$ -invariant if $h(x)$ is in the tangent space of $x$ for all $h$ in $D_{E}$ and $x$ in $X$. We show that $X$ is $D_{E}$ -invariant if and only if it is the union of $E$-orbits. For such $X$, we define first integrals and construct a quotient space for the $E$-action. An important case occurs when $G$ is an algebraic subgroup of $GL(V$) and $E$ consists of the $G$-equivariant polynomial endomorphisms. In this case, the associated $D_{E}$ is the space the $G$-invariant vector fields. A significant question here is whether there are non-constant $G$-invariant first integrals on $X$. As examples, we study the adjoint representation, orbit closures of highest weight vectors, and representations of the additive group. We also look at finite-dimensional irreducible representations of SL2 and its nullcone.

Endomorphism Semigroups of Some Class of Connected Unars with Stagnant Element

The class $$\mathfrak{K}$$ of all connected unars with stagnant element being their single knot element is considered. Structure of the endomorphism semigroups of unars from $$\mathfrak{K}$$ is described.

Completely Decomposable Quotient Divisible Abelian Groups with Isomorphic Endomorphism Semigroups

Let $$\Lambda$$ be a class of Abelian groups. A group $$A\in\Lambda$$ is said to be determined by its endomorphism semigroup $$E^\star(A)$$ in the class $$\Lambda$$ if every isomorphism $$E^\star(A)\cong E^\star(B)$$ , where $$B\in\Lambda$$ , implies the isomorphism $$A\cong B$$ . The paper describes those Abelian groups in the class $$\mathscr Q\mathscr D_{\mathrm{cd}}$$ of completely decomposable quotient divisible Abelian groups which are determined by their endomorphism semigroups in the class $$\mathscr Q\mathscr D_{\mathrm{cd}}$$ .

On automorphisms of the semigroup of endomorphisms of a free abelian dimonoid

On automorphisms of the semigroup of endomorphisms of a free abelian dimonoid

Free rectangular doppelsemigroups

A doppelsemigroup is a nonempty set equipped with two binary associative operations satisfying certain identities. In this paper, we consider the variety of rectangular doppelsemigroups which are analogs of rectangular semigroups. We construct the free rectangular doppelsemigroup and characterize the least rectangular congruence on the free doppelsemigroup. As a consequence, the free rectangular semigroup is presented. We also describe all (maximal) subdoppelsemigroups, all idempotents and all endomorphisms of the free rectangular doppelsemigroup, and give a criterion for an isomorphism of endomorphism semigroups of free rectangular doppelsemigroups. In addition, we show that the endomorphism semigroup of the free rectangular doppelsemigroup is not regular in general.

On concrete characterization problem of endomorphism semigroups of graphs

For endomorphism semigroups of graphs we investigate the following concrete characterization problem: under which conditions is a transformation semigroup S equal to the endomorphism semigroup $$\mathop {\mathrm{End}}\nolimits G$$ of some quasi-acyclic reflexive graph G.

On automorphisms of the semigroup of endomorphisms of a free abelian dimonoid

On automorphisms of the semigroup of endomorphisms of a free abelian dimonoid

Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups

Let C be an Abelian group. A class X of Abelian groups is called a CE•H-class if, for every groups A, B ∈ X, the isomorphisms E•(A) ≅ E•(B) and Hom(C, A) ≅ Hom(C, B) imply the isomorphism A ≅ B. In the paper, necessary and sufficient conditions on a completely decomposable torsion-free Abelian group C are described under which a given class of torsion-free Abelian groupsisa CE•H-class.