共查询到10条相似文献,搜索用时 125 毫秒
1.
Jimmie D. Lawson 《Geometriae Dedicata》1998,70(2):139-180
The Möbius semigroup studied in this paper arises very naturally geometrically as the (compression) subsemigroup of the group of Möbius transformations which carry some fixed open Möbius ball into itself. It is shown, using geometric arguments, that this semigroup is a maximal subsemigroup. A detailed analysis of the semigroup is carried out via the Lorentz representation, in which the semigroup resurfaces as the semigroup carrying a fixed half of a Lorentzian cone into itself. Close ties with the Lie theory of semigroups are established by showing that the semigroup in question admits the structure of an Ol'shanskii semigroup, the most widely studied class of Lie semigroups. 相似文献
2.
Emil Daniel Schwab 《代数通讯》2013,41(5):1779-1789
We study the incidence algebra of the reduced standard division category of a combinatorial bisimple inverse monoid [with (E(S), ≤) locally finite], and we describe semigroups of poset type (i.e., a combinatorial inverse semigroup for which the corresponding Möbius category is a poset) as being combinatorial strict inverse semigroups. Up to isomorphism, the only Möbius-division categories are the reduced standard division categories of combinatorial inverse monoids. 相似文献
3.
4.
\noindent
The purpose of this paper is to point out some aspects of the
relationship between combinatorial inverse semigroups and their
Möbius categories, and to explore combinatorial results arising
from combinatorial Brandt semigroups, fundamental simple inverse
-semigroups and from the free monogenic inverse
semigroup. 相似文献
5.
设A是代数闭域k上的一个具乘基B的有限维含幺结合代数,称半群B∪{0}为A的基半群.本文给出了0 J 严格单半群的定义.对于基半群为0 J 严格单半群的零直并的代数,完全研究了它的代数表示型 相似文献
6.
Alexei Vernitski 《Semigroup Forum》2009,78(3):486-497
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. 相似文献
7.
Benjamin Steinberg 《Advances in Mathematics》2010,223(2):689-727
Let K be a commutative ring with unit and S an inverse semigroup. We show that the semigroup algebra KS can be described as a convolution algebra of functions on the universal étale groupoid associated to S by Paterson. This result is a simultaneous generalization of the author's earlier work on finite inverse semigroups and Paterson's theorem for the universal C∗-algebra. It provides a convenient topological framework for understanding the structure of KS, including the center and when it has a unit. In this theory, the role of Gelfand duality is replaced by Stone duality.Using this approach we construct the finite dimensional irreducible representations of an inverse semigroup over an arbitrary field as induced representations from associated groups, generalizing the case of an inverse semigroup with finitely many idempotents. More generally, we describe the irreducible representations of an inverse semigroup S that can be induced from associated groups as precisely those satisfying a certain “finiteness condition.” This “finiteness condition” is satisfied, for instance, by all representations of an inverse semigroup whose image contains a primitive idempotent. 相似文献
8.
E-Ehresmann semigroups are a commonly studied generalization of inverse semigroups. They are closely related to Ehresmann categories in the same way that inverse semigroups are related to inductive groupoids. We prove that under some finiteness condition, the semigroup algebra of an E-Ehresmann semigroup is isomorphic to the category algebra of the corresponding Ehresmann category. This generalizes a result of Steinberg who proved this isomorphism for inverse semigroups and inductive groupoids and a result of Guo and Chen who proved it for ample semigroups. We also characterize E-Ehresmann semigroups whose corresponding Ehresmann category is an EI-category and give some natural examples. 相似文献
9.
We define a convolution-like operator which transforms functions on a space X via functions on an arithmetical semigroup S, when there is an action or flow of S on X. This operator includes the well-known classical Möbius transforms and associated inversion formulas as special cases. It is defined in a sufficiently general context so as to emphasize the universal and functorial aspects of arithmetical Möbius inversion. We give general analytic conditions guaranteeing the existence of the transform and the validity of the corresponding inversion formulas, in terms of operators on certain function spaces. A number of examples are studied that illustrate the advantages of the convolutional point of view for obtaining new inversion formulas. 相似文献
10.
R. Exel 《Semigroup Forum》2009,79(1):159-182
By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse
semigroup
in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of
Booleanness present in the semilattice of idempotents of
. After observing that the Vagner–Preston representation is not tight, we exhibit a canonical tight representation for any
inverse semigroup with zero, called the regular tight representation. We then tackle the question as to whether this representation is faithful, but it turns out that the answer is often negative.
The lack of faithfulness is however completely understood as long as we restrict to continuous inverse semigroups, a class generalizing the E
*-unitaries.
Partially supported by CNPq. 相似文献