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1.
In this paper, we investigate the pseudo-amenability of semigroup algebra ? 1(S), where S is an inverse semigroup with uniformly locally finite idempotent set. In particular, we show that for a Brandt semigroup \(S={\mathcal{M}}^{0}(G,I)\), the pseudo-amenability of ? 1(S) is equivalent to the amenability of G.  相似文献   

2.
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   

3.
In this paper, we characterize pseudo-contractibility of 1(S), where S is a uniformly locally finite inverse semigroup. As a consequence, we show that for a Brandt semigroup S=M0(G,I),{S={\mathcal{M}}^{0}(G,I),} the semigroup algebra 1(S) is pseudo-contractible if and only if G and I are finite. Moreover, we study the notions of pseudo-amenability and pseudo-contractibility of a semigroup algebra 1(S) in terms of the amenability of S.  相似文献   

4.
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   

5.
In this paper we compare the notions of super amenability and super module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. We find conditions for the two notions to be equivalent. In particular, we study arbitrary module actions of l 1(E S ) on l 1(S) for an inverse semigroup S with the set of idempotents E S and show that under certain conditions, l 1(S) is super module amenable if and only if S is finite. We also study the super module amenability of l 1(S)?? and module biprojectivity of l 1(S), for arbitrary actions.  相似文献   

6.
In this work, we will describe the weighted semigroup algebra ? 1(S, ω), where S is a regular Rees matrix semigroup and ω ≥  1. Then as an application, we investigate the amenability of the semigroup algebra ? 1(S, ω) and its second dual for an arbitrary semigroup S.  相似文献   

7.
We shall study the biflatness of the convolution algebra  1(S) for a semigroup S. We show that for any semigroup S such that  1(S) is biflat the canonical partial ordering on the idempotents must be uniformly locally finite. We use this to characterize the biflatness of  1(S) for an inverse semigroup S.  相似文献   

8.
Let C be a small category. Then we consider 1(C) as the 1 algebra over the morphisms of C, with convolution product and also consider as the 1 algebra over the objects of C, with pointwise multiplication. The main purpose of this paper is to show that approximate amenability of 1(C) implies of and clearly this implies that C has only finitely many objects. Some applications are given, the main one is the characterization of approximate amenability for 1(S), where S is a Brandt semigroup, which corrects a result of Lashkarizadeh Bami and Samea (Semigroup Forum 71:312–322, 2005).  相似文献   

9.
In this paper we introduce the notion of module character amenable Banach algebras and show that they possess module character virtual (approximate) diagonals. As a basic example, we show that for an inverse semigroup S with the set of idempotents E, the semigroup algebra ? 1(S) is module character amenable as an ? 1(E)-module if only if S is amenable.  相似文献   

10.
For any finite commutative idempotent semigroup S, a semilattice, we show how to compute the amenability constant of its semigroup algebra 1(S). This amenability constant is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. We also give example of a commutative Clifford semigroups G n whose semigroup algebras 1(G n ) admit amenability constants of the form 41+4(n−1)/n. We also show there is no commutative semigroup whose semigroup algebra has an amenability constant between 5 and 9. N. Spronk’s research was supported by NSERC Grant 312515-05.  相似文献   

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