Is every locally compact abelian group which admits a symplectic self-duality isomorphic to the product of a locally compact abelian group and its Pontryagin dual? Several sufficient conditions, covering all the typical applications are found. Counterexamples are produced by studying a seemingly unrelated question about the structure of maximal isotropic subgroups of finite abelian groups with ...

In [10], we study solutions to the affine normal flow for an initial hypersurface L ⊂ R which is a convex, properly embedded, noncompact hypersurface. The method we used was to consider an exhausting sequence Li of smooth, strictly convex, compact hypersurfaces so that each Li is contained in the convex hull of Li+1 for each i, and so that Li → L locally uniformly. If the compact Li is the init...

Consider a closed subgroup H of a locally compact group G together with a strongly continuous unitary representation u of H on a Hilbert space K. The construction of the induced representation uses these three ingredients to supply a new strongly continuous unitary representation ρ of the larger group G on a new Hilbert space K. Induced group representations for finite groups where first introd...

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

Write S = {z ∈ C : |z| = 1}. A character of a locally compact abelian group G is a continuous group homomorphism G → S. We denote by Ĝ the set of characters of G, where for φ1, φ2 ∈ Ĝ and x ∈ G, we define (φ1φ2)(x) = φ1(x)φ2(x). We assign Ĝ the final topology for the family of functions {φ 7→ φ(x) : x ∈ G}, i.e., the coarsest topology on Ĝ so that for each x ∈ G, the function φ 7→ φ(x) is conti...

Let G be a locally compact group equipped with a left Haar measure μ, i.e. a Borel regular measure which is finite on compact, positive on open and invariant under left multiplications — by Haar’s theorem such μ exists and is unique up to normalization. The group G is called unimodular if μ is also right invariant, or equivalently if it is symmetric in the sense that μ(A) = μ(A−1) for every mea...