Deformed Fomin-Kirillov Algebras and Applications
Deformierte Fomin-Kirillov-Algebren und Anwendungen
Bastian
Röhrig
Group
Nichols algebra
Mathematics
symmetric group
Hopf algebra
Algebra
Mathematics
Mathematik
We consider a deformed version of Fomin-Kirillov algebras and investigate their relation to regular Fomin-Kirillov algebras. We observe that certain subalgebras of a deformed Fomin-Kirillov algebra closely resemble "smaller" Fomin-Kirillov algebras. This observation is used to calculate the vector space dimension of Fomin-Kirillov algebras in many examples, in particular for the complete graph on 5 vertices. Furthermore, we study groups attached to Fomin-Kirillov algebras. The attached groups turn out to posses striking structures in examples.
Philipps-Universität Marburg
Marburg
Deutschhausstraße 9, 35037 Marburg
István
Heckenberger
Prof. Dr.
2016
2016-12-21
2017-01-12
2022-02-01
Text
doctoralThesis
urn:nbn:de:hebis:04-z2017-00493
eng
thesis.doctoral
Philipps-Universität Marburg
Marburg
1
https://archiv.ub.uni-marburg.de/diss/z2017/0049/pdf/dbr.pdf
10.17192/z2017.0049
https://archiv.ub.uni-marburg.de/diss/z2017/0049
https://rightsstatements.org/vocab/InC-NC/1.0/