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Non-Resonant Uniserial Representations of Vec(R)

The non-resonant bounded uniserial representations of Vec(R) form a certain class of extensions composed of tensor density modules, all of whose subquotients are indecomposable. The problem of classifying the extensions with a given composition series is reduced via cohomological methods to computing the solution of a certain system of polynomial equations in several variables derived from the cup equations for the extension. Using this method, we classify all non-resonant bounded uniserial extensions of Vec(R) up to length 6. Beyond this length, all such extensions appear to arise as subquotients of extensions of arbitrary length, many of which are explained by the psuedodifferential operator modules. Others are explained by a wedge construction and by the pseudodifferential operator cocycle discovered by Khesin and Kravchenko.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc1157650
Date05 1900
CreatorsO'Dell, Connor
ContributorsConley, Charles H., Brozovic, Douglas P., Shepler, Anne V.
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatvi, 140 pages, Text
RightsPublic, O'Dell, Connor, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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