let s be a semigroup. in certain cases we give some characterizations of extreme amenability of s and we show that in these cases extreme left amenability and extreme right amenability of s are equivalent. also when s is a compact topological semigroup, we characterize extremely left amenable subalgebras of c(s), where c(s) is the space of all continuous bounded real valued functions on s

let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is de ned. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

This paper corrects the statement and the proof of Theorem 1.5 of the paper quoted in the title (Represent. Theory 13 (2009), 427–459). Theorem 1.5 of our paper [1] requires a correction. Below we provide a new statement of this theorem and correct the proof. A mistake in the original proof of Theorem 1.5 is due to missing the multiple 2 at a certain point of the proof (see [1, page 456, line 2...

Abstract We study the boundary behaviour of solutions u of −∆Nu + |u| u = 0 in a bounded smooth domain Ω ⊂ R subject to the boundary condition u = 0 except at one point, in the range q > N − 1. We prove that if q ≥ 2N − 1 such a u is identically zero, while, if N − 1 < q < 2N − 1, u inherits a boundary behaviour which either corresponds to a weak singularity, or to a strong singularity. Such si...

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...

For any n ∈ N such that 2n ≤ min(p, q), we construct a representation πn of O(p, q) with p+q even as the kernel of a commuting set of n(n+1) 2 number of O(p, q)-invariant differential operators in the space of C∞ functions on an isotropic cone with a distinguished GLn(R)-homogeneity degree. By identifying πn with a certain representation constructed via the formalism of the theta correspondence...

Abstract We give a combinatorial characterization of amenability monomial algebras and prove the existence Følner sequences, answering question due to Ceccherini–Silberstein Samet–Vaillant. then use our that over projectively simple algebras, every module is exhaustively amenable; we conclude convolution minimal subshifts admit same property. deduce any subshift positive entropy gives rise grad...

We obtain a presentation of the principal subspace of the basic A (2) 2n –module, n ≥ 1. We show that its full character is given by the Nahm sum of the tadpole Dynkin diagram Tn = A2n/Z2. This character is conjecturally modular after certain specializations. We prove the modularity property in the case of the affine Lie algebra of type A (2) 4 .