On the representation theory of braided Hopf-algebras.

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...

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Bibliographic Details
Main Author: Alia, Abdalla
Contributors: Heckenberger, István (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2022
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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.
Physical Description:86 Pages
DOI:10.17192/z2022.0112