Quantum function algebras from finite-dimensional Nichols algebras

We describe how to find quantum determinants and antipode formulas from braided vector spaces using the FRT-construction and finite-dimensional Nichols algebras. It generalizes the construction of quantum function algebras using quantum grassmanian algebras. Given a finite-dimensional Nichols algebr...

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Detalles Bibliográficos
Autores principales: Farinati, Marco A., García, Gastón Andrés
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2020
Materias:
Matemática
Quantum function algebras
Nichols algebras
Quantum determinants
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/129665
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-129665
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Quantum function algebras
Nichols algebras
Quantum determinants
spellingShingle Matemática
Quantum function algebras
Nichols algebras
Quantum determinants
Farinati, Marco A.
García, Gastón Andrés
Quantum function algebras from finite-dimensional Nichols algebras
topic_facet Matemática
Quantum function algebras
Nichols algebras
Quantum determinants
description We describe how to find quantum determinants and antipode formulas from braided vector spaces using the FRT-construction and finite-dimensional Nichols algebras. It generalizes the construction of quantum function algebras using quantum grassmanian algebras. Given a finite-dimensional Nichols algebra B, our method provides a Hopf algebra H such that B is a braided Hopf algebra in the category of H-comodules. It also serves as source to produce Hopf algebras generated by cosemisimple subcoalgebras, which are of interest for the generalized lifting method. We give several examples, among them quantum function algebras from Fomin-Kirillov algebras associated with the symmetric groups on three letters.
format Articulo
Preprint
author Farinati, Marco A.
García, Gastón Andrés
author_facet Farinati, Marco A.
García, Gastón Andrés
author_sort Farinati, Marco A.
title Quantum function algebras from finite-dimensional Nichols algebras
title_short Quantum function algebras from finite-dimensional Nichols algebras
title_full Quantum function algebras from finite-dimensional Nichols algebras
title_fullStr Quantum function algebras from finite-dimensional Nichols algebras
title_full_unstemmed Quantum function algebras from finite-dimensional Nichols algebras
title_sort quantum function algebras from finite-dimensional nichols algebras
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/129665
work_keys_str_mv AT farinatimarcoa quantumfunctionalgebrasfromfinitedimensionalnicholsalgebras
AT garciagastonandres quantumfunctionalgebrasfromfinitedimensionalnicholsalgebras
bdutipo_str Repositorios
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