Cohomology and extensions of representations of groups with normal Engel subgroups

Kissin, Edward and Shulman, Victor (2023) Cohomology and extensions of representations of groups with normal Engel subgroups. European Journal of Mathematics. ISSN 2199-6768 (In Press)

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Abstract / Description

Let λ, U be representations of a group G with a normal subgroup N. The paper studies the first cohomology group H1 (G, λ, U) under various spectral type conditions imposed on the restrictions of λ, U to N. We assume often that N is an Engel group and examine various decompositions of the extension e(λ, U, ξ) of λ by U associated with non-trivial (λ, U)-cocycles ξ.
Aiming at applications to double extensions and the theory of J-unitary group representations on indefinite metric spaces, we describe (λ, U)-cocycles when G = D n N is the semidirect product, D is an Engel group and the restrictions of λ, U to N are χ1 for some character χ on N (such pairs of representations form in a sense a base class in the variety of all pairs of representations). Our description is complete if G = D n Rn, where D is the group of all diagonal matrices with positive entries, or G = D n T is the group of all upper triangular matrices d = (dij ) with dii > 0 and T is its subgroup of all matrices with dii = 1, or G = SO(2) n R2.
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Item Type:	Article
Uncontrolled Keywords:	Cohomology, Representations, Engel, group, extension of representations
Subjects:	500 Natural Sciences and Mathematics > 510 Mathematics
Department:	School of Computing and Digital Media
Depositing User:	Edward Kissin
Date Deposited:	04 Jul 2023 08:21
Last Modified:	04 Jul 2023 08:21
URI:	https://repository.londonmet.ac.uk/id/eprint/8622

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