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...

The conjecture that every algebra norm || • || on C(X) is equivalent to the uniform norm arises naturally from a theorem of Kaplansky in 1949 that necessarily 11/11 > \f\x ( ƒ e C(X)): see [9, 10.1]. The seminal paper on the automatic continuity of homomorphisms from C(X) is the 1960 paper of Bade and Curtis [2] in which, for example, it is proved that there is a discontinuous homomorphism from...

LetA be a finite-dimensional commutative algebra over the complex numbers with nonzero multiplicative identity element e. Let M denote the set of homomorphisms from A onto the complex numbers. Thus we get a homomorphism from A into the algebra of complex-valued functions on M, with respect to pointwise addition and multiplication of functions, by sending an element x of A to the function on M w...

4 Conjectures and results 12 4.1 The symmetry conjecture . . . . . . . . . . . . . . . . . . . . . . 12 4.2 Othogonal idempotents and character formulas . . . . . . . . . . 15 4.3 The double coset conjecture . . . . . . . . . . . . . . . . . . . . . 17 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.5 The case of a single generator . . . . . . . . . . . . . . ...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

In [2], A.Alekseev and E.Meinrenken construct an explicit G-differential space homomorphism Q, called the quantization map, between the Weil algebra Wg = S(g ) ⊗ ∧(g) and Wg = U (g) ⊗ Cl(g) (which they called the noncommutative Weil algebra) for any quadratic Lie algebra g. They showed that Q induces an algebra isomorphism between the basic cohomology rings H bas(Wg) and H ∗ bas(Wg). In this pa...

Let G be a smooth affine group over a field k, and λ : Gm → G a k-homomorphism (possibly trivial, though that case is not interesting). One often calls λ a 1-parameter k-subgroup of G, even when kerλ 6= 1. Such a homomorphism defines a left action of Gm on G via the functorial procedure t.g = λ(t)gλ(t)−1 for g ∈ G(R) and t ∈ R× for any k-algebra R. In lecture we introduced the following associa...

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

Every finite dimensional Hopf algebra is a Frobenius algebra, with Frobenius homomorphism given by an integral. The Nakayama automorphism determined by it yields a decomposition with degrees in a cyclic group. For a family of pointed Hopf algebras, we determine necessary and sufficient conditions for this decomposition to be strongly graded.