Finite-dimensional Nichols algebras over dual Radford algebras
For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe the simple objects in Hn,m Hn,m YD and their projective envelopes. Then, we d...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/150434 |
| Acceso en línea: | http://hdl.handle.net/11336/150434 |
| Access Level: | acceso abierto |
| Palabra clave: | DUAL RADFORD HOPF ALGEBRA HOPF ALGEBRA NICHOLS ALGEBRA STANDARD FILTRATION https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe the simple objects in Hn,m Hn,m YD and their projective envelopes. Then, we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case n = 2. There are 18 possible cases. We present by generators and relations the corresponding Nichols algebras on five of these eighteen cases. As an application, we characterize finite-dimensional Nichols algebras over indecomposable modules for n = 2 = m and n = 2, m = 3, which recovers some results of the second and third author in the former case, and of Xiong in the latter. |
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