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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 identity λ(x, st) = λ(x.s, t)λ(x, s), almost everywhere 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 among 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:	Refereed Article
Keywords:	separable locally compact groups, modular function, quasi-invariant measure, lambda-function
Research Division:	Mathematical Sciences
Research Group:	Pure mathematics
Research Field:	Group theory and generalisations
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the mathematical sciences
UTAS Author:	Dharmadasa, HK (Dr Kumudini Dharmadasa)
ID Code:	130896
Year Published:	2018
Deposited By:	Mathematics and Physics
Deposited On:	2019-02-19
Last Modified:	2019-06-12
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