On a Class of Factorizable Inverse Monoids Associated with Braid Groups

We prove that a constructible nilpotent-by-abelian group G can be obtained from a polycyclic group by forming d successive properly ascending HNN-extensions if and only if d is the dimension of the linear subspace of Hom(G, R) spanned by the geometric invariant Σ¹ (G, Z) ^c . We also obtain a result on the finiteness properties “type FP _m ” of certain subgroups of G     

Homomorphisms of Finitary Incidence Algebras

For any field K and poset P, the incidence space I(P) and the finitary incidence algebra FI(P) were introduced in [5 Khripchenko , N. , Novikov , B. ( 2009 ). Finitary incidence algebras . Communications in Algebra 37 : 1670 – 1676 . [Google Scholar]]. The K-vector space I(P) is an FI(P)-bimodule. We investigate K-linear maps from FI(P) to I(P) that preserve submodules. We also consider the idealization FI(P)(+)I(P) of I(P).     

Multiplicative Automorphisms of Incidence Algebras

We present necessary and sufficient conditions for a multiplicative automorphism of an incidence algebra of a finite partially ordered set X to be an inner automorphism. These conditions are related to the structure of X as a directed graph.     

Classification of Involutions on Incidence Algebras

For the case when a finite partially ordered set X has an element that is comparable with all the elements of X, we present necessary and sufficient conditions for two involutions on the incidence algebra of X (over a field of characteristic different from 2) to be equivalent via inner automorphism. Furthermore, we use this classification to get the general classification of involutions.     

Quotients of Incidence Algebras and the Euler Characteristic

In this note, we show that, if A ? kQ _A /I _A is a schurian strongly simply connected algebra given by its normed presentation, and Σ is the unique poset whose Hasse quiver coincides with Q _A , then A ? kΣ if and only if I _A has a generating set consisting of exactly χ(Q _A ) elements, where χ(Q _A ) is the Euler characteristic of Q _A . We also prove that a quotient of an incidence algebra A = kΣ/J is strongly simply connected if and only if A is simply connected and kΣ is strongly simply connected.     

Computing the Hochschild Cohomology Groups of Some Families of Incidence Algebras

The purpose of this article is to present some computations of Hochschild cohomology groups of particular classes of incidence algebras using one-point extensions and one-point coextensions.     

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。     

含幺逆半群的半格的同余对

本文利用一族含幺逆半群的同余对刻画了其半格的同余对,并给出了含幺逆半群半格的正规同余对族的格与其标准同余对的格之间的同构关系.     

Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions

In this paper, we consider a multiplicative convolution operator $${{\cal M}_     

Elementary and Good Group Gradings of Incidence Algebras over Partially-Ordered Sets with Cross-Cuts

Let G be a group, X a locally-finite partially-ordered set, and F a field. We provide an algorithmic method for finding all good G-gradings of the incidence algebra I(X,F) when X has a cross-cut of length one or two. In these cases, we show that the good gradings are determined by a “freeness” property. It is shown that the number of good gradings of the incidence algebra I(X,F), when X has a cross-cut of length one or two, depends only on the size of G and not on its structure, but this is no longer true when the shortest cross-cut of X has length greater than two. If X has a cross-cut of length one, then every good grading of I(X,F) is an elementary grading, but, when the shortest cross-cut of X has length greater than one, there may exist good gradings of I(X,F) that are not elementary gradings. Finally, we establish bounds on the number of good gradings of I(X,F) for any finite partially-ordered set X.     

Inverse semigroups and combinatorial C*-algebras

We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term tight. These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the tight spectrum, which is in turn shown to be precisely the closure of the space of ultra-filters, once filters are identified with semicharacters in a natural way. These representations are moreover shown to correspond to representations of the C*-algebra of the groupoid of germs for the action of S on its tight spectrum. We then treat the case of certain inverse semigroups constructed from semigroupoids, generalizing and inspired by inverse semigroups constructed from ordinary and higher rank graphs. The tight representations of this inverse semigroup are in one-to-one correspondence with representations of the semigroupoid, and consequently the semigroupoid algebra is given a groupoid model. The groupoid which arises from this construction is shown to be the same as the boundary path groupoid of Farthing, Muhly and Yeend, at least in the singly aligned, sourceless case. *Partially supported by CNPq.     

On Some Geometric Representations of GL N (𝔬)

We study a family of complex representations of the group GL _n (𝔬), where 𝔬 is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL _n (F) to its maximal compact subgroup GL _n (𝔬). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra associated with the representation and an algebraic basis that consists of its minimal idempotents. The transition matrix involves combinatorial invariants of lattices of submodules of finite 𝔬-modules. The idempotents are p-adic analogs of the multivariable Jacobi polynomials.