Root multiplicities for Nichols Algebras of diagonal type

Root multiplicities for Nichols Algebras of diagonal type

In this thesis we chase the root multiplicities for Nichols algebras of diagonal type. Based on an inequality for the number of Lyndon words and an identity for the shuffle map, we illustrate when the multiplicity of a root is smaller than in the tensor algebra of a braided vector space of diagonal...

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Bibliografiske detaljer
Hovedforfatter: Zheng, Ying
Andre forfattere: Heckenberger, Istvan (Prof. Dr.) (BetreuerIn (Doktorarbeit))
Format: Dissertation
Sprog:engelsk
Udgivet: Philipps-Universität Marburg 2018
Fag:
Lyndon-Wörter
multiplicities
Lyndon words
Mathematik
Multiplizitäten
root
Wurzel
Nichols-Algebren
Nichols algebras
Mathematics
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Beskrivelse
Summary:In this thesis we chase the root multiplicities for Nichols algebras of diagonal type. Based on an inequality for the number of Lyndon words and an identity for the shuffle map, we illustrate when the multiplicity of a root is smaller than in the tensor algebra of a braided vector space of diagonal type, and determine the dimension of the kernel of the shuffle map considered as an operator acting on the free algebra. Moreover, we give an complete expression for the multiplicities of a class of roots for Nichols algebras of diagonal type of rank two.
Fysisk beskrivelse:91 Seiten
DOI:10.17192/z2018.0491

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