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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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Bibliographic Details
Main Author: Röhrig, Bastian
Contributors: Heckenberger, István (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2016
Subjects:
Hopf-Algebra
Symmetrische Gruppe
Hopf algebra
Group
Gruppe <Mathematik>
Algebra
Nichols-Algebra
Mathematik
symmetric group
Mathematics
Nichols algebra
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Description
Summary: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.
Physical Description:107 Pages
DOI:10.17192/z2017.0049

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