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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
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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