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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Bibliographic Details
Main Author: Zheng, Ying
Contributors: Heckenberger, Istvan (Prof. Dr.) (Thesis advisor)
Format: Dissertation
Language:English
Published: Philipps-Universität Marburg 2018
Mathematik und Informatik
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Online Access:PDF Full Text
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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.
Physical Description:91 Pages
DOI:https://doi.org/10.17192/z2018.0491