Deformed Fomin-Kirillov Algebras and Applications

Deformed Fomin-Kirillov Algebras and Applications

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 th...

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Bibliografische gegevens
Hoofdauteur: Röhrig, Bastian
Andere auteurs: Heckenberger, István (Prof. Dr.) (Thesis begeleider)
Formaat: Dissertation
Taal:Engels
Gepubliceerd in: Philipps-Universität Marburg 2016
Onderwerpen:
Hopf-Algebra
Group
Nichols algebra
Symmetrische Gruppe
Gruppe <Mathematik>
Nichols-Algebra
Algebra
Mathematics
Mathematik
symmetric group
Hopf algebra
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Samenvatting: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.
Fysieke beschrijving:107 Seiten
DOI:10.17192/z2017.0049

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