C-algebras of Inverse Semigroups: Amenability and Weak Containment
نویسنده
چکیده
We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism φ of S onto a group G, we show, under an assumption on ker(φ), that S has weak containment if and only if G is amenable and ker(φ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show that all graph inverse semigroups have weak containment and that Nica’s inverse semigroup TG,P of a quasi-lattice ordered group (G, P ) has weak containment if and only if (G, P ) is amenable.
منابع مشابه
p-Analog of the Semigroup Fourier-Steiltjes Algebras
In this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.
متن کاملModule approximate amenability of Banach algebras
In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...
متن کامل2n-Weak module amenability of semigroup algebras
Let $S$ be an inverse semigroup with the set of idempotents $E$. We prove that the semigroup algebra $ell^{1}(S)$ is always $2n$-weakly module amenable as an $ell^{1}(E)$-module, for any $nin mathbb{N}$, where $E$ acts on $S$ trivially from the left and by multiplication from the right. Our proof is based on a common fixed point property for semigroups.
متن کاملNuclearity of Semigroup C*-algebras and the Connection to Amenability
We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclear...
متن کامل$(-1)$-Weak Amenability of Second Dual of Real Banach Algebras
Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on $ A_mathbb{C} $ satisfying a simple condition together with the norm $ | cdot | $ on $ A$. In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006