We find a one parameter family of quadratic Poisson structures on R 4 × SL(2, C) which satisfies the property a) that it is preserved under the Lie-Poisson action of the Lorentz group, as well as b) that it reduces to the standard Poincaré algebra for a particular limiting value of the parameter. (The Lie-Poisson transformations reduce to canonical ones in that limit, which we therefore refer t...

A basic problem in the theory of Lie algebra extensions concerns a given homomorphism x of a Lie algebra L into the Lie algebra of outer derivations of a Lie algebra B . In analogy with the theory of group extensions, Mori and HochschiId developed the concept of an obstruction to x being the homomorphism defined by some Lie algebra extension of B by L . This note considers an alternative approa...

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...

Let *3* be the algebra of polynomials in one indeterminate x over the complex field C. Suppose || • || is a norm on 9 such that the coefficient functionals c,: X a.oc' —* a, (j = 0,1,2, • • •) are all continuous with respect to || • ||, and let K CC be the set of characters on 9> which are || • ||-continuous. Then K is compact, C\K is connected, and 0 G K. Let A be the completion of 9 with resp...

We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as for example those given by Poisson or contact structures, but we consider degenerate structures as well. Introduction We shall admit different classes of smoothness, so by a manifold of ...

We consider contractive homomorphisms of a planar algebra A(Ω) over a finitely connected bounded domain Ω ⊆ C and ask if they are necessarily completely contractive. We show that a homomorphism ρ : A(Ω) → B(H) for which dim(A(Ω)/ ker ρ) = 2 is the direct integral of homomorphisms ρT induced by operators on two dimensional Hilbert spaces via a suitable functional calculus ρT : f 7→ f(T ), f ∈ A(...

Following E. Kirchberg, [3], we call a bifunctor (A,B) → A⊗α B a C -algebraic tensor product functor if it is obtained by completing of the algebraic tensor product A ⊙ B of C-algebras in a functional way with respect to a suitable C-norm ‖ · ‖α. We call such a functor symmetric if the standard isomorphism A ⊙ B ∼= B ⊙ A extends to an isomorphism A⊗αB ∼= B⊗αA. Similarly, we call it associative ...

Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.

We give the nuclear analogue of Dadarlat’s characterization of exact quasidiagonal C∗-algebras. Specifically, we prove the following: Theorem 0.1. Let A be a unital separable simple C∗-algebra. Then the following conditions are equivalent: i) A is nuclear and quasidiagonal. ii) A has the stabilization principle. iii) If π : A → M(A ⊗ K) is a unital, purely large ∗-homomorphism, then the image π...

Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C| = BC. We study the ring homomorphism HH∗(kC) → H∗(|C|, k) and prove it is split surjective, using the factorization category of Quillen [16] and certain techniques from functor cohomology theory. This generalizes the well-known results for finite groups...