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Titel:On the representation theory of braided Hopf-algebras.
Autor:Alia, Abdalla
Weitere Beteiligte: Heckenberger, István (Prof. Dr.)
Veröffentlicht:2022
URI:https://archiv.ub.uni-marburg.de/diss/z2022/0112
DOI: https://doi.org/10.17192/z2022.0112
URN: urn:nbn:de:hebis:04-z2022-01128
DDC:510 Mathematik
Publikationsdatum:2022-05-25
Lizenz:https://rightsstatements.org/vocab/InC-NC/1.0/

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Summary:
The body of work is designed for the representation theory of deformed Fomin-Kirillov algebras using Gabriel’s theorem. In particular, we proved that for the spacial case of n= 4. The basic deformation admits a decomposition into Nil-Coxeter algebras of type S4 while the non-basic deformation admits a graded “deformation” of a symmetric algebra. Furthermore, we studied special types of subalgebras based on subgraphs. In particular, We proved that the sub-algebras based on Dynkin type quiver are isomorphic to Iwahori-Hecke algebras and concluded with providing an equivalence for the the semisimpicity of the sub-algebra based on type D_4.


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