Artículo
On pointed Hopf algebras over nilpotent groups
Fecha de publicación:
06/2023
Editorial:
Hebrew Univ Magnes Press
Revista:
Israel Journal Of Mathematics
ISSN:
0021-2172
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We classify finite-dimensional Nichols algebras over finite nilpotent groups of odd order in group-theoretical terms. The main step is to show that the conjugacy classes of such finite groups are either abelian or of type C; this property also holds for finite conjugacy classes of finitely generated nilpotent groups whose torsion has odd order. To extend our approach to the setting of finite GK-dimension, we propose a new Conjecture on racks of type C. We also prove that the bosonization of a Nichols algebra of a Yetter-Drinfeld module over a group whose support is an infinite conjugacy class has infinite GK-dimension. We apply this to the study of the finite GK-dimensional pointed Hopf algebras over finitely generated torsion-free nilpotent groups.
Palabras clave:
Hopf algebras
,
Nichols algebras
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Andruskiewitsch, Nicolas; On pointed Hopf algebras over nilpotent groups; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 6-2023; 1-34
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