FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2808876239> ?p ?o ?g. }

• W2808876239 abstract "This dissertation arose from efforts to investigate an example which appeared in (G) of a phenomenon which has been considered to be rare: namely, the existence of two discrete cocompact subgroups $Gammasb1$ and $Gammasb2$ in a Lie group G such that $Gammasb1/G$ and $Gammasb2/G$ have the same (unitary) spectrum but $Gammasb1$ is not isomorphic to $Gammasb2.$ This phenomenon may be called representation equivalence of $Gammasb1$ and $Gammasb2$ with $Gammasb1$ non-isomorphic to $Gammasb2.$. In (G) the first known example of this phenomenon in the class of solvable Lie groups was given. In this example G was a specific three-step nilpotent Lie group and two discrete cocompact subgroups $Gammasb1$ and $Gammasb2$ of G such that $Gammasb1$ is representation equivalent to $Gammasb2$ with non-isomorphic to $Gammasb2$ were presented. In the present dissertation we have been able to generalize this example and prove the following result: Let G be any three-step nilpotent Lie algebra with rational structure constants and all coadjoint orbits flat. Then there exist discrete cocompact subgroups $Gammasb1$ and $Gammasb2$ in G such that $Gammasb1$ is representation equivalent to $Gammasb2$ but $Gammasb1$ is not isomorphic to $Gammasb2.$. This theorem contains the example in (G) as a special case and demonstrates that this phenomenon occurs surprisingly often. Chapter 2 contains the proof of this new result. The author investigated the role of flatness of orbits in this phenomenon of non-isomorphic representation equivalence by considering the lowest dimensional example of a nilpotent Lie group with non-flat coadjoint orbits. The author has been able to show that for a large category of discrete cocompact subgroups of this group this phenomenon of non-isomorphic representation equivalence cannot occur. Chapter 3 contains the proof of this result. The author has also proven some short but apparently new structural results for three-step nilpotent Lie groups with one-dimensional center. Chapter 4 contains these. Chapter 1 contains the background material for the work undertaken in Chapters 2, 3 and 4." @default.
• W2808876239 created "2018-06-29" @default.
• W2808876239 creator A5064720657 @default.
• W2808876239 date "2022-06-14" @default.
• W2808876239 modified "2023-10-07" @default.
• W2808876239 title "On the Relationship Between Representation Equivalence and Isomorphism of Fundamental Groups of Three-Step Nilmanifolds." @default.
• W2808876239 cites W1598666130 @default.
• W2808876239 cites W1990419938 @default.
• W2808876239 cites W2035284983 @default.
• W2808876239 cites W2069306484 @default.
• W2808876239 cites W2091438642 @default.
• W2808876239 cites W2332219236 @default.
• W2808876239 cites W2629603438 @default.
• W2808876239 doi "https://doi.org/10.31390/gradschool_disstheses.6056" @default.
• W2808876239 hasPublicationYear "2022" @default.
• W2808876239 type Work @default.
• W2808876239 sameAs 2808876239 @default.
• W2808876239 citedByCount "0" @default.
• W2808876239 crossrefType "dissertation" @default.
• W2808876239 hasAuthorship W2808876239A5064720657 @default.
• W2808876239 hasBestOaLocation W28088762391 @default.
• W2808876239 hasConcept C115624301 @default.
• W2808876239 hasConcept C121332964 @default.
• W2808876239 hasConcept C185592680 @default.
• W2808876239 hasConcept C187915474 @default.
• W2808876239 hasConcept C202444582 @default.
• W2808876239 hasConcept C203436722 @default.
• W2808876239 hasConcept C33923547 @default.
• W2808876239 hasConcept C50335755 @default.
• W2808876239 hasConcept C50555996 @default.
• W2808876239 hasConcept C62520636 @default.
• W2808876239 hasConcept C8010536 @default.
• W2808876239 hasConceptScore W2808876239C115624301 @default.
• W2808876239 hasConceptScore W2808876239C121332964 @default.
• W2808876239 hasConceptScore W2808876239C185592680 @default.
• W2808876239 hasConceptScore W2808876239C187915474 @default.
• W2808876239 hasConceptScore W2808876239C202444582 @default.
• W2808876239 hasConceptScore W2808876239C203436722 @default.
• W2808876239 hasConceptScore W2808876239C33923547 @default.
• W2808876239 hasConceptScore W2808876239C50335755 @default.
• W2808876239 hasConceptScore W2808876239C50555996 @default.
• W2808876239 hasConceptScore W2808876239C62520636 @default.
• W2808876239 hasConceptScore W2808876239C8010536 @default.
• W2808876239 hasLocation W28088762391 @default.
• W2808876239 hasOpenAccess W2808876239 @default.
• W2808876239 hasPrimaryLocation W28088762391 @default.
• W2808876239 hasRelatedWork W2256043873 @default.
• W2808876239 hasRelatedWork W2291386138 @default.
• W2808876239 hasRelatedWork W2952605465 @default.
• W2808876239 hasRelatedWork W2981695848 @default.
• W2808876239 hasRelatedWork W3184611687 @default.
• W2808876239 hasRelatedWork W4293059793 @default.
• W2808876239 hasRelatedWork W4300366167 @default.
• W2808876239 hasRelatedWork W4301724906 @default.
• W2808876239 hasRelatedWork W4386794951 @default.
• W2808876239 hasRelatedWork W4947501 @default.
• W2808876239 isParatext "false" @default.
• W2808876239 isRetracted "false" @default.
• W2808876239 magId "2808876239" @default.
• W2808876239 workType "dissertation" @default.