共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Wadii Hajji 《代数通讯》2013,41(12):5261-5281
The aim in this article is to provide a parametrization of the finite dimensional irreducible representations of a compact inverse semigroup in terms of the irreducible representations of maximal subgroups and order theoretic properties of the idempotent set. As a consequence, we obtain a new, and more conceptual, proof of the following theorem of Shneperman: a compact inverse semigroup has enough finite dimensional irreducible representations to separate points if and only if its idempotent set is totally disconnected. Moreover, we also prove that every norm continuous irreducible *-representation of a compact inverse semigroup on a Hilbert space is finite dimensional. 相似文献
3.
A. V. Rukolaine 《Journal of Mathematical Sciences》1982,20(6):2657-2664
For elements of a finite inverse semigroup, an equivalence relation called p-conugacy is introduced. It is proved that for any matrix representation of a finite inverse semigroup the values of the character of the representation are equal on p-conjugate elements. The number of inequivalent irreducible matrix representations of a finite inverse semigroup over the field of complex numbers is equal to the number of classes of p-conjugate elements.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 207–215, 1977. 相似文献
4.
5.
In a paper published in 1994, Umar defined an interesting class of transformation semigroups which naturally generalizes the Vagner one-point completion of the symmetric inverse semigroup. In this paper we prove some isomorphism theorems for finite such semigroups and compute their ranks. Moreover, we determine all maximal inverse subsemigroups of an arbitrary transformation semigroup of this type which is not inverse. 相似文献
6.
In this article, the approximate amenability of semigroup algebra ?1(S) is investigated, where (S) is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup (S), the notions of amenability, approximate amenability and bounded approximate amenability of ?1(S) are equivalent. We use this to give a direct proof of the approximate amenability of ?1(S) for a Brandt semigroup (S). Moreover, we characterize the approximate amenability of ?1(S), where S is a uniformly locally finite band semigroup. 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.
Pedro V. Silva 《代数通讯》2013,41(6):2482-2494
An inverse semigroup S is a Howson inverse semigroup if the intersection of finitely generated inverse subsemigroups of S is finitely generated. Given a locally finite action θ of a group G on a semilattice E, it is proved that E*θG is a Howson inverse semigroup if and only if G is a Howson group. It is also shown that this equivalence fails for arbitrary actions. 相似文献
9.
N. A. Nemirovskaya 《Mathematical Notes》1997,61(2):201-205
In the paper, the problem of representing a finite inverse semigroup by partial transformations of a graph is treated. The
notions of weighted graph and its weighted partial isomorphisms are introduced. The main result is that any finite inverse
semigroup is isomorphic to the semigroup of weighted partial isomorphisms of a weighted graph. This assertion is a natural
generalization of the Frucht theorem for groups.
Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 246–251, February, 1997.
This research was partially supported by the International Science Foundation under grant No. GSU 041049.
Translated by A. I. Shtern 相似文献
10.
11.
Benjamin Steinberg 《Journal of Combinatorial Theory, Series A》2006,113(5):866-881
This paper explores several applications of Möbius functions to the representation theory of finite semigroups. We extend Solomon's approach to the semigroup algebra of a finite semilattice via Möbius functions to arbitrary finite inverse semigroups. This allows us to explicitly calculate the orthogonal central idempotents decomposing an inverse semigroup algebra into a direct product of matrix algebras over group rings. We also extend work of Bidigare, Hanlon, Rockmore and Brown on calculating eigenvalues of random walks associated to certain classes of finite semigroups; again Möbius functions play an important role. 相似文献
12.
Yingdan Ji 《代数通讯》2013,41(12):5149-5162
Let S be a finite orthodox semigroup or an orthodox semigroup where the idempotent band E(S) is locally pseudofinite. In this paper, by using principal factors and Rukolaǐne idempotents, we show that the contracted semigroup algebra R0[S] is semiprimitive if and only if S is an inverse semigroup and R[G] is semiprimitive for each maximal subgroup G of S. This theorem strengthens previous results about the semiprimitivity of inverse semigroup algebras. 相似文献
13.
We show that all of the Schützenberger complexes of an Adian inverse semigroup are finite if the Schützenberger complex of every positive word is finite. This enables us to solve the word problem for certain classes of Adian inverse semigroups (and hence for the corresponding Adian semigroups and Adian groups). 相似文献
14.
S.M. Maepa 《Quaestiones Mathematicae》2016,39(3):307-318
We study the character amenability of semigroup algebras. We work on general semigroups and certain semigroups such as inverse semigroups with a finite number of idempotents, inverse semigroups with uniformly locally finite idempotent set, Brandt and Rees semigroup and study the character amenability of the semigroup algebra l1(S) in relation to the structures of the semigroup S. In particular, we show that for any semigroup S, if ?1(S) is character amenable, then S is amenable and regular. We also show that the left character amenability of the semigroup algebra ?1(S) on a Brandt semigroup S over a group G with index set J is equivalent to the amenability of G and J being finite. Finally, we show that for a Rees semigroup S with a zero over the group G, the left character amenability of ?1(S) is equivalent to its amenability, this is in turn equivalent to G being amenable. 相似文献
15.
V. D. Derech 《Ukrainian Mathematical Journal》2012,63(9):1390-1399
For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms
are permutable. 相似文献
16.
V. D. Derech 《Ukrainian Mathematical Journal》2010,62(1):31-42
We establish necessary and sufficient conditions for any stable order on a finite inverse semigroup with zero to be fundamental
or antifundamental. 相似文献
17.
We formulate an alternative approach to describing Ehresmann semigroups by means of left and right étale actions of a meet semilattice on a category. We also characterize the Ehresmann semigroups that arise as the set of all subsets of a finite category. As applications, we prove that every restriction semigroup can be nicely embedded into a restriction semigroup constructed from a category, and we describe when a restriction semigroup can be nicely embedded into an inverse semigroup.
相似文献18.
Amal AlAli 《代数通讯》2017,45(11):4667-4678
19.
James East 《代数通讯》2013,41(5):1671-1689
We give a semigroup presentation of the singular part of the symmetric inverse monoid on a finite set. Along the way, we derive a monoid presentation of the monoid of all order-preserving injective partial transformations on a finite chain, which differs from the presentation discovered by Fernandes. 相似文献
20.
Every inverse semigroup possesses a natural partial order and therefore convexity with respect to this order is of interest.
We study the extent to which an inverse semigroup is determined by its lattice of convex inverse subsemigroups; that is, if
the lattices of two inverse semigroups are isomorphic, how are the semigroups related? We solve this problem completely for
semilattices and for inverse semigroups in general reduce it to the case where the lattice isomorphism induces an isomorphism
between the semilattices of idempotents of the semigroups. For many inverse semigroups, such as the monogenic ones, this case
is the only one that can occur. In Part II, a study of the reduced case enables us to prove that many inverse semigroups,
such as the free ones, are strictly determined by their lattices of convex inverse subsemigroups, and to show that the answer
obtained here for semilattices can be extended to a broad class of inverse semigroups, including all finite, aperiodic ones.
Received September 24, 2002; accepted in final form December 15, 2002. 相似文献