Locally compact topologies on a group and the corresponding continuous irreducible representations
نویسندگان
چکیده
منابع مشابه
Relations between positive definite functions and irreducible representations on a locally compact groupoid
If G is a locally compact groupoid with a Haar system λ, then a positive definite function p on G has a form p(x) = 〈L(x)ξ(d(x)), ξ(r(x))〉, where L is a representation of G on a Hilbert bundle H = (G, {Hu}, μ), μ is a quasi invariant measure on G 0 and ξ ∈ L(G,H). [10]. In this paper firt we prove that if μ is a quasi invariant ergodic measure on G, then two corresponding representations of G a...
متن کاملTopologies Corresponding to Continuous Representability of Preorders
A topology τ on a fixed nonempty set X is said to satisfy the weakly continuous representation property if every weakly continuous not necessarily total preorder on the topological space (X, τ) admits a continuous order preserving function. Such a property generalizes the well known continuous representation property of a topology τ on a set X (according to which every continuous total preorder...
متن کاملCoherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus
We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of antiholomorphic sections in which the irreducible Hermitian representations of the original algebra are realized. The reproducing kernels of these spaces are express...
متن کاملOn continuous cohomology of locally compact Abelian groups and bilinear maps
Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...
متن کاملCompact Group Topologies for R
There is a compact solenoidal group S that is group isomorphic to the additive real numbers R. The existence of 5 leads to a study of compact real groups; that is, compact groups which are group isomorphic to R. The compact real groups are characterized as products of 5. Various conditions on a topological group G are given which are equivalent to G being compact real. It is shown that any comp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1969
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1969.31.583