Representations of a noncommutative and noncocommutative bialgebra: quantum version

Snehashis Mukherjee

doi:10.5802/crmath.820

Article de recherche - Algèbre

Representations of a noncommutative and noncocommutative bialgebra: quantum version
[Représentations d’une bigèbre non commutative et non cocommutative : version quantique]

Snehashis Mukherjee ¹

¹Indian Institute of Technology, Kanpur, Kalyanpur, Kanpur, Uttar Pradesh, 208016, India

Comptes Rendus. Mathématique, Volume 364 (2026), pp. 79-86

Abstract (VO)
Résumé

In this article we classify all simple modules over a noncommutative and noncocommutative bialgebra $M(p,q)$ assuming $q$ is a root of unity.

Dans cet article, nous classifions tous les modules simples sur une bigèbre non commutative et non cocommutative $M(p,q)$, en supposant que $q$ est une racine de l’unité.

Reçu le : 2025-03-22
Révisé le : 2025-11-22
Accepté le : 2026-01-26
Publié le : 2026-03-09

DOI : 10.5802/crmath.820

Classification : 16D60, 16D70, 16S85
Keywords: Simple modules, polynomial identity algebra, Smith normal form, eigenvalue analysis, noncommutative and noncocommutative bialgebra
Mots-clés : Modules simples, algèbre à identité polynomiale, forme normale de Smith, analyse des valeurs propres, bigèbre non commutative et non cocommutative

Affiliations des auteurs :

Snehashis Mukherjee ¹

¹ Indian Institute of Technology, Kanpur, Kalyanpur, Kanpur, Uttar Pradesh, 208016, India

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Snehashis Mukherjee},
     title = {Representations of a noncommutative and noncocommutative bialgebra: quantum version},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {79--86},
     year = {2026},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {364},
     doi = {10.5802/crmath.820},
     language = {en},
}

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Snehashis Mukherjee. Representations of a noncommutative and noncocommutative bialgebra: quantum version. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 79-86. doi: 10.5802/crmath.820

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