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...

Täydet tiedot

Tallennettuna:
Bibliografiset tiedot
Päätekijä: Röhrig, Bastian
Muut tekijät: Heckenberger, István (Prof. Dr.) (BetreuerIn (Doktorarbeit))
Aineistotyyppi: Dissertation
Kieli:englanti
Julkaistu: Philipps-Universität Marburg 2016
Aiheet:
Hopf-Algebra
Group
Nichols algebra
Symmetrische Gruppe
Gruppe <Mathematik>
Nichols-Algebra
Algebra
Mathematics
Mathematik
symmetric group
Hopf algebra
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Yhteenveto: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.
Ulkoasu:107 Seiten
DOI:10.17192/z2017.0049

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