Integrals in Hopf algebras over rings

• Tipo: Artigo em Revista Científica Internacional
• Data: 2004

Autores

Lomp, Christian (Autor) FCUP

Revista

Título: Communications in Algebra

Vol. 32 Nº 12

Páginas: 4687-4711

ISSN: 0092-7872

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 11 Citações

Scopus - 10 Citações

Outras Informações

ID Authenticus: P-000-CF9

DOI: 10.1081/agb-200036837

Abstract (EN): Integrals in Hopf algebras are an essential tool in studying finite dimensional Hopf algebras and their action on rings. Over fields it has been shown by Sweedler that the existence of integrals in a Hopf algebra is equivalent to the Hopf algebra being finite dimensional. In this paper we examine how much of this is true Hopf algebras over rings. We show that over any commutative ring R that is not a field there exists a Hopf algebra H over R containing a non-zero integral but not being finitely generated as R-module. On the contrary we show that Sweedler's equivalence is still valid for free Hopf algebras or projective Hopf algebras over integral domains. Analogously for a left H-module algebra A we study the influence of non-zero left A#H-linear maps from A to A#H on H being finitely generated as R-module. Examples and application to separability are given.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 25