Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension

Istvan  Heckenberger; Ehud Meir; Leandro  Vendramin

doi:10.1016/j.aim.2024.109637

Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension

Istvan Heckenberger, Ehud Meir, Leandro Vendramin^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

Abstract

Over fields of characteristic zero, we determine all absolutely irreducible Yetter–Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided vector spaces and study their degenerations and specializations.

Original language	English
Article number	109637
Number of pages	30
Journal	Advances in Mathematics
Volume	444
DOIs	https://doi.org/10.1016/j.aim.2024.109637
Publication status	Published - May 2024

Bibliographical note

Acknowledgements. EM would like to thank Ben Martin for fruitful discussions about geometric invariant theory in positive characteristic

Keywords

Nichols algebra
Affine rack
Alexander rack
braiding
Braiding

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Heckenberger_etal_AM_Finite_Dimensional_Nichols_AAM
This manuscript has been made open access under a Creative Commons Attribution (CC BY) licence under the terms of the University of Aberdeen Research Publications Policy. https://creativecommons.org/licenses/by/4.0/ Final published version available at https://doi.org/10.1016/j.aim.2024.109637
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Cite this

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title = "Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension",

abstract = "Over fields of characteristic zero, we determine all absolutely irreducible Yetter–Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided vector spaces and study their degenerations and specializations.",

keywords = "Nichols algebra, Affine rack, Alexander rack, braiding, Braiding",

author = "Istvan Heckenberger and Ehud Meir and Leandro Vendramin",

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AU - Heckenberger, Istvan

AU - Meir, Ehud

AU - Vendramin, Leandro

N1 - Acknowledgements. EM would like to thank Ben Martin for fruitful discussions about geometric invariant theory in positive characteristic

PY - 2024/5

Y1 - 2024/5

N2 - Over fields of characteristic zero, we determine all absolutely irreducible Yetter–Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided vector spaces and study their degenerations and specializations.

AB - Over fields of characteristic zero, we determine all absolutely irreducible Yetter–Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided vector spaces and study their degenerations and specializations.

KW - Nichols algebra

KW - Affine rack

KW - Alexander rack

KW - braiding

KW - Braiding

UR - http://www.scopus.com/inward/record.url?scp=85189761437&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2024.109637

DO - 10.1016/j.aim.2024.109637

M3 - Article

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VL - 444

JO - Advances in Mathematics

JF - Advances in Mathematics

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ER -

Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension

Abstract

Bibliographical note

Keywords

Access to Document

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