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An identity for cocycles on coset spaces of locally compact groups
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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 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: | Article |
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Authors/Creators: | Dharmadasa, HK and Moran, W |
Keywords: | separable locally compact groups, modular function, quasi-invariant measure, lambda-function |
Journal or Publication Title: | Rocky Mountain Journal of Mathematics |
Publisher: | Rocky Mt Math Consortium |
ISSN: | 0035-7596 |
DOI / ID Number: | 10.1216/RMJ-2018-48-1-269 |
Copyright Information: | Copyright 2018 Rocky Mountain Mathematics Consortium |
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Item Statistics: | View statistics for this item |
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