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http://dx.doi.org/10.18419/opus-11536
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DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Truong, Monika | - |
dc.date.accessioned | 2021-06-16T10:28:29Z | - |
dc.date.available | 2021-06-16T10:28:29Z | - |
dc.date.issued | 2018 | de |
dc.identifier.other | 1760585939 | - |
dc.identifier.uri | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-115535 | de |
dc.identifier.uri | http://elib.uni-stuttgart.de/handle/11682/11553 | - |
dc.identifier.uri | http://dx.doi.org/10.18419/opus-11536 | - |
dc.description.abstract | A group corresponds to a topological space with one nontrivial homotopy group. A crossed module corresponds to a topological space with two nontrivial homotopy groups. In classical group theory, Cayley's Theorem constructs for every group G an injective group morphism to the symmetric group S_G. For a crossed module V, we have a similar statement. For every category C, we have the symmetric crossed module S_C. For every crossed module V, we construct an injective crossed module morphism to the symmetric crossed module S_VCat. Suppose given an R-linear category M. On the one hand, we obtain the invertible monoidal category Aut_R(M) by means of category theory. On the other hand, we have the symmetric crossed module S_M as in the Cayley context. In S_M, we have the crossed submodule Aut^CM_R(M) containing only the R-linear elements of S_M. We consider the corresponding invertible monoidal category (Aut^CM_R(M))Cat. We show that there exists a monoidal isofunctor Real_M : (Aut^CM_R(M))Cat -~-> Aut_R(M). This means that starting with M, we obtain essentially the same object via crossed module theory as via category theory. A representation of a group G on an R-module N is given by a group morphism G -> Aut_R(N). Analogously, a representation of a crossed module V on an R-linear category M is given by a crossed module morphism V -> Aut^CM_R(M). We begin to study the representation theory of crossed modules. | en |
dc.language.iso | en | de |
dc.rights | info:eu-repo/semantics/openAccess | de |
dc.subject.ddc | 510 | de |
dc.title | Basic representation theory of crossed modules | en |
dc.type | masterThesis | de |
ubs.fakultaet | Mathematik und Physik | de |
ubs.institut | Fakultät Mathematik und Physik (Institutsübergreifend) | de |
ubs.publikation.seiten | xvi, 196 | de |
ubs.publikation.typ | Abschlussarbeit (Master) | de |
Enthalten in den Sammlungen: | 08 Fakultät Mathematik und Physik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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master_truong_monika_pdfa.pdf | 1,28 MB | Adobe PDF | Öffnen/Anzeigen |
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