Open Access Repository
An identity for cocycles on coset spaces of locally compact groups
Downloads
Downloads per month over past year

|
PDF
AnIdentityForCo...pdf | Download (238kB) | Preview |
Abstract
We prove here an identity for cocycles associated with homogeneous spaces in the context of locally compact groups. Mackey introduced cocycles (λ-functions) in his work on representation theory of such groups. For a given locally compact group G and a closed subgroup H of G, with right coset space G/H, a cocycle λ is a real-valued Borel function on G/H × G satisfying the cocycle identityλ(x; st) = λ(x.s,t)λ(x,s), a.e. x ∈ G/H,s,t∈G,where the "almost everywhere" is with respect to a measure whose null sets pull back to Haar measure null sets on G. Let H and K be regularly related closed subgroups of G. Our identity describes a relationship between cocycles for G/Hx, G/Ky and G/(Hx∩Ky) for almost all x,y ∈ G. This also leads to an identity for modular functions of G and the corresponding subgroups.
Item Type: | Article |
---|---|
Authors/Creators: | Dharmadasa, HK and Moran, W |
Keywords: | separable locally compact groups, quasi-invariant measures, modular function, lambda function |
Journal or Publication Title: | Rocky Mountain Journal of Mathematics |
Publisher: | Rocky Mt Math Consortium |
ISSN: | 0035-7596 |
Copyright Information: | Copyright 2017 the publisher |
Related URLs: | |
Item Statistics: | View statistics for this item |
Actions (login required)
![]() |
Item Control Page |