Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590000 | Journal of Functional Analysis | 2015 | 47 Pages |
Abstract
Let λ be a finite-dimensional representation of a connected nilpotent group G and U be a unitary representation of G. We investigate the structure of the extensions of λ by U and, correspondingly, the group H1(λ,U)H1(λ,U) of 1-cohomologies. A spectral criterion of triviality of H1(λ,U)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)(λ,U)-cocycles – neutral cocycles, which play a crucial role in the theory of J -unitary representations of groups on Pontryagin ΠkΠk-spaces.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Edward Kissin, Victor S. Shulman,