Maximal Inverse Subsemigroups of the Symmetric Inverse Semigroup on a Finite-Dimensional Vector Space

The notion of “near isomorphism” for torsion-free Abelian groups of finite rank is well known. In particular, this concept turned out to be of importance for classifying almost completely decomposable groups. We extend near isomorphism to classes of torsion-free Abelian groups of infinite rank which are unions of bcd–groups, this is to say unions of groups which are bounded essential extensions of completely decomposable groups. Moreover, we show that nearly isomorphic groups of this class also have nearly isomorphic endomorphism rings considered as Abelian groups.     

一类逆半群的嵌入定理

给出了一类特殊的E*-酉逆半群——适当逆半群的一个嵌入定理.     

含幺逆半群的半格上的同余格

本文证明了含幺逆半群Sα（α∈Y）的半格的容许同余格同构于半格S上同余格的一个子格。     

Inverse Subsemigroups of the Monogenic Free Inverse Semigroup

It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proven to be decidable.     

A Trace-Like Invariant for Representations of Hopf Algebras

We introduce an invariant for the irreducible representations of finite dimensional Hopf algebras, defined as the trace of a map induced by the antipode on the endomorphisms of each corresponding simple module. We also compute the value of this invariant for the representations of two families of non-semisimple Hopf algebras.     

The Translational Hull of Strongly Inverse Wrpp Semigroups

In this paper,we obtain some characterizations of the translational hull of strongly inverse wrpp semigroups.And we prove that the translational hull of a strongly inverse wrpp semigroup is still of the same type.     

逆差商的一个紧凑行列式表示

本文给出了逆差商的一个紧凑行列式表示,从该表示式易知,一个函数在某ｎ＋１个点的ｎ阶逆差商与这些点的排序有关,但与前ｎ－１个点的局部换序无关．此外,还从另一角度定义倒差商,得出了倒差商与逆差商之间的关系以及倒差商的整体换序无关性．     

On a Finite Difference Scheme for an Inverse Integro-Differential Problem Using Semigroup Theory: A Functional Analytic Approach

In this article, the problem of reconstructing an unknown memory kernel from an integral overdetermination in an abstract linear (of convolution type) evolution equation of parabolic type is considered. After illustrating some results of the existence and uniqueness of a solution for the differential problem, we study its approximation by Rothe's method. We prove a result of stability and another concerning the order of approximation of the solution in dependence of its regularity. The main tool is a maximal regularity result for solutions to abstract parabolic finite difference schemes. Two model problems to which the results are applicable are illustrated.     

Inverse subsemigroups and classes of finite aperiodic semigroups

We prove a number of results related to finite semigroups and their inverse subsemigroups, including the following. (1) A finite semigroup is aperiodic if and only if it is a homomorphic image of a finite semigroup whose inverse subsemigroups are semilattices. (2) A finite inverse semigroup can be represented by order-preserving mappings on a chain if and only if it is a semilattice. Finally, we introduce the concept of pseudo-small quasivariety of finite semigroups, generalizing the concept of small variety.     

The Local Structure of Graded Representations

In this article we show that the local structure of the projective representation space of a graded algebra can locally be described by quivers with an automorphism of their path algebra, a weighted twist. We describe the quotient spaces of these weighted twisted quiver settings and determine which of them are smooth.     

The Automata that Define Representations of Monomial Algebras

It is well known that the sets of strings that define all representations of string algebras and many representations of other quotients of path algebras form a regular set, and hence are defined by finite state automata. This short article aims to explain this connection between representation theory and automata theory in elementary terms; no technical background in either representation theory or automata theory is assumed. The article describes the structure of the set of strings of a monomial algebra as a locally testable and hence regular set, and describes explicitly the construction of the automaton, illustrating the construction with an elementary example. Hence it explains how the sets of strings and bands of a monomial algebra correspond to the sets of paths and closed (non-powered) circuits in a finite graph, and how the growth rate of the set of bands is immediately visible from that graph. Presented by C. Ringel.     

On Representations of Affine Hecke Algebras of Type B

Ariki’s and Grojnowski’s approach to the representation theory of affine Hecke algebras of type A is applied to type B with unequal parameters to obtain – under certain restrictions on the eigenvalues of the lattice operators – analogous multiplicity-one results and a classification of irreducibles with partial branching rules as in type A. Research supported by the Studienstiftung des deutschen Volkes.     

On the classification of partition quantum groups

This is a survey on some results obtained recently in the classification of compact quantum groups associated to partitions, with a focus on the non-crossing case. We take a global look at the main results in the subject and highlight some key features of the methods used. We conclude by several suggestions for pushing further the classification.     

Normal Domain Representations of Topological Spaces

D′ ⊆ D is a normal totality on a Scott domain D if it is upward closed and x ⊓ y ∈ D′ is an equivalence relation on D′. We prove that every topological space can be represented by a domain with norma totality.     

Rees Matrix Covers and the Translational Hull of a Locally Inverse Semigroup

For any locally inverse semigroup S, there exists a maximal dense ideal extension of S within the class LI of all locally inverse semigroups (Pastijn and Oliveira, 2006 Pastijn , F. J. , Oliveira , L. ( 2006 ). Maximal dense ideal extensions of locally inverse semigroups . Semigroup Forum 72 : 441 – 458 . [Google Scholar], Preprint). Here we realize this maximal dense ideal extension in terms of a canonically constructed quotient of a regular Rees matrix semigroup over an inverse semigroup.     

Representations of a pair of posets

In this article we determine the pairs of posets which are finitely represented.Supported by State Education Commission.     

Heart of Irreducible Morphisms of Bounded Complexes

In [9 Giraldo , H. , Merklen , H. ( 2009 ). Irreducible morphisms of categories of complexes . Journal of Algebra 321 : 2716 – 2736 .[Crossref], [Web of Science ®] , [Google Scholar]] Giraldo and Merklen studied irreducible morphisms in the categories 𝒞(𝒜) and D^?(Λ), where 𝒞(𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and D^?(Λ) is the derived category of the bounded above complexes of finite generate left modules, over an Artin algebra Λ. In this work, we continue the study of irreducible morphism having one finite irreducible truncation.     

乘法半群上的线性方程组与晶体对势的反演

用乘法半群上的线性方程组来求解晶体原子间对势反演的逆问题.这种方法是解决此类问题的一般性方法.本文还给出了一个计算实例.