# An identity for cocycles on coset spaces of locally compact groups

Dharmadasa, HK ORCID: 0000-0003-2869-799X and Moran, W 2017 , 'An identity for cocycles on coset spaces of locally compact groups' , Rocky Mountain Journal of Mathematics , pp. 1-5 .

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## 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 Dharmadasa, HK and Moran, W separable locally compact groups, quasi-invariant measures, modular function, lambda function Rocky Mountain Journal of Mathematics Rocky Mt Math Consortium 0035-7596 Copyright 2017 the publisher UTAS Profile: Dharmadasa, HK View statistics for this item