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An identity for cocycles on coset spaces of locally compact groups
Citation
Dharmadasa, HK and Moran, W, An identity for cocycles on coset spaces of locally compact groups, Rocky Mountain Journal of Mathematics, 48, (1) pp. 269-277. ISSN 0035-7596 (2018) [Refereed Article]
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Copyright Statement
Copyright 2018 Rocky Mountain Mathematics Consortium
DOI: doi:10.1216/RMJ-2018-48-1-269
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 Details
Item Type: | Refereed Article |
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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 |
Downloads: | 0 |
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