Lifting of Quantum Linear Spaces and Pointed Hopf Algebras of order p3 / Nicolás Andruskiewitsch, Hans-Jürgen Schneider.
Idioma: Inglés Series Trabajos de Matemática. Serie A / Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física ; no. 48Detalles de publicación: Córdoba, Argentina : Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 1997.Descripción: 28 p. ; 30 cmTema(s): Resumen: We propose the following principle to study pointed Hopf algebras, or more generally, Hopf algebras whose coradical is a Hopf subalgebra.Given such a Hopf algebra A, consider its coradical filtration and the associated graded coalgebra gr A. Then gr A is a graded Hopf algebra, since the coradical A0 of A is a Hopf subalgebra. In addition, there is a projection π: gr A → A0; let R be the algebra of coinvariants of π. Then, by a result of Radford and Majid, R is a braided Hopf algebra and gr A is the bosonization (or biproduct) of Rand A0: gr A similar, equals R#A0. The principle we propose to study A is first to study R, then to transfer the information to gr A via bosonization, and finally to lift to A. In this article, we apply this principle to the situation when R is the simplest braided Hopf algebra: a quantum linear space. As consequences of our technique, we obtain the classification of pointed Hopf algebras of order p3(pan odd prime) over an algebraically closed field of characteristic zero; with the same hypothesis, the characterization of the pointed Hopf algebras whose coradical is abelian and has index p or p2; and an infinite family of pointed, non- isomorphic, Hopf algebras of the same dimension. This last result gives a negative answer to a conjecture of I. Kaplansky.Tipo de ítem | Biblioteca actual | Signatura | Copia número | Estado | Notas | Fecha de vencimiento | Código de barras | Reserva de ítems |
---|---|---|---|---|---|---|---|---|
Series FaMAF | FaMAF Sección Series Famaf | Trabajo Matemática Serie A CAJA 4 - F0136 | 1 | Disponible | F0136 | |||
Series FaMAF | FaMAF Sección Series Famaf | Trabajo Matemática Serie A CAJA 4 - F0137 | 2 | Disponible | Versión corregida en Journal of Algebra vol. 209, no.2, p. 658-691(1998). | F0137 |
Versión corregida en Journal of Algebra vol. 209, no.2, p. 658-691(1998).
Bibliografía : p. 28.
We propose the following principle to study pointed Hopf algebras, or more generally, Hopf algebras whose coradical is a Hopf subalgebra.Given such a Hopf algebra A, consider its coradical filtration and the associated graded coalgebra gr A. Then gr A is a graded Hopf algebra, since the coradical A0 of A is a Hopf subalgebra. In addition, there is a projection π: gr A → A0; let R be the algebra of coinvariants of π. Then, by a result of Radford and Majid, R is a braided Hopf algebra and gr A is the bosonization (or biproduct) of Rand A0: gr A similar, equals R#A0. The principle we propose to study A is first to study R, then to transfer the information to gr A via bosonization, and finally to lift to A. In this article, we apply this principle to the situation when R is the simplest braided Hopf algebra: a quantum linear space. As consequences of our technique, we obtain the classification of pointed Hopf algebras of order p3(pan odd prime) over an algebraically closed field of characteristic zero; with the same hypothesis, the characterization of the pointed Hopf algebras whose coradical is abelian and has index p or p2; and an infinite family of pointed, non- isomorphic, Hopf algebras of the same dimension. This last result gives a negative answer to a conjecture of I. Kaplansky.
Texto en inglés.