Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles

Kissin, Edward and Shulman, Victor S. (2015) Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles. Journal of Functional Analysis, 269 (8). pp. 2564-2610. ISSN 0022-1236

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Official URL: http://dx.doi.org/10.1016/j.jfa.2015.07.003

Abstract

Let λbe a finite-dimensional representation of a connected nilpotent group Gand Ube a unitary representation of G. We investigate the structure of the extensions of λby Uand, correspondingly, the group H1(λ, U)of 1-cohomologies. A spectral criterion of triviality of H1(λ, U)is proved and systematically used in the study of various types of decomposition of the extensions. We consider a special type of (λ, U)-cocycles – neutral cocycles, which play a crucial role in the theory of J-unitary representations of groups on Pontryagin Πk-spaces.

Item Type: Article
Uncontrolled Keywords: Nonunitary representation; Nilpotent group; Cohomology; Extension; Cocycle
Subjects: 500 Natural Sciences and Mathemetics > 510 Mathematics
Department: School of Computing and Digital Media
Depositing User: Edward Kissin
Date Deposited: 16 Jun 2016 11:27
Last Modified: 12 Oct 2016 09:16
URI: http://repository.londonmet.ac.uk/id/eprint/1013

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