this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper studies the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture together with Atiyah’s L-index theorem implies that the range consists of the integers. We give a direct and elementary proof that if G acts ...

The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper studies the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture together with Atiyah’s L-index theorem implies that the range consists of the integers. We give a direct and elementary proof that if G acts ...

which for every finite Galois extension L/K induces an isomorphism invL/K : H (Gal(L/K), L×) ∼ −→ 1 [L:K]Z/Z via composition with the inflation map Inf : H2(Gal(L/K), L×)→ H2(Gal(Ksep/K),Ksep×), and we showed that invK is canonical and natural in K; see Theorem 30.25 In this lecture we will use the invariant map to define the local Artin homomorphism and prove the local version of Artin recipro...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...

For a frame $L$, consider the $f$-ring $ mathcal{F}_{mathcal P}L=Frm(mathcal{P}(mathbb R), L)$. In this paper, first we show that each minimal ideal of $ mathcal{F}_{mathcal P}L$ is a principal ideal generated by $f_a$, where $a$ is an atom of $L$. Then we show that if $L$ is an $mathcal{F}_{mathcal P}$-completely regular frame, then the socle of $ mathcal{F}_{mathcal P}L$ consists of those $f$...

Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from affine super Yangian [Formula: see text] to universal enveloping algebra of rectangular W-superalgebra for all m ≠ n, m, n ≥ 2 or 3, = 0. Furthermore, show that image this is dense, provided k + ( − n)( l 1)

The aim of this paper is to show that any continuous ∗-homomorphism of L(C)(with twisted convolution as multiplication) into B(L(R)) is essentially a Weyl transform. From this we deduce a similar characterisation for the group Fourier transform on the Heisenberg group, in terms of convolution.

We use the results on the minimal basis of the centre of an Iwahori–Hecke algebra from our earlier work, as well as some additional results on the minimal basis, to describe the image and kernel of the Brauer homomorphism for Iwahori–Hecke algebras defined by L. Jones (Jones, L. Centres of Generic Hecke Algebras; Ph.D. Thesis; University of Virginia, 1987.).