Dokument: Hom-Tensor Adjunktionen fuer Quasi-Hopfalgebren

Titel:	Hom-Tensor Adjunktionen fuer Quasi-Hopfalgebren
Weiterer Titel:	Hom-Tensor Adjunctions for Quasi-Hopf Algebras
URL für Lesezeichen:	https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=9547
URN (NBN):	urn:nbn:de:hbz:061-20081105-105818-8
Kollektion:	Dissertationen
Sprache:	Englisch
Dokumententyp:	Wissenschaftliche Abschlussarbeiten » Dissertation
Medientyp:	Text
Autor:	Bagheri, Saeid [Autor]
Dateien:	[Dateien anzeigen] Adobe PDF [Details] 731,7 KB in einer Datei [ZIP-Datei erzeugen] Dateien vom 05.11.2008 / geändert 05.11.2008
Dewey Dezimal-Klassifikation:	500 Naturwissenschaften und Mathematik
Beschreibung:	For a commutative ring k, the category of k-modules is monoidal and the tensor-functor is a left adjoint to the Hom-functor. If H is a k-bialgebra, then the category of left H-modules is monoidal with the same associativity constraint. This yields tensor functors as endofunctors of H-Mod. If H is a Hopf algebra, then for H-module V, we obtain Hom-functor Hom (V,-) as endofunctor H-Mod which is right adjoint to the Tensor-functor. Over a bialgebra H, a right Hopf module M has a right module and a right comodule structure which are compatible. In this case, the comparison functor is an equivalence of categories if and only if H is a Hopf algebra ( Fundamental Theorem for Hopf algebras ). This thesis is concerned with quasi-bialgebras defined by Drinfeld (in 1990) by requiring the same axioms as for bialgebras except for the coassociativity condition of the coproduct which is modified by a normalized 3-cocycle. Similar to the case of Hopf algebras, the category of modules over a quasi-bialgebra H is monoidal. But in this case, the associativity constraint is no longer the trivial one. The notion of an antipode was adapted to a quasi-antipodeby Drinfeld in a way that guarantees the rigidity of modules in the finite case. The Fundamental Theorem corresponds to the comparison functor being an equivalence. The inverse has been obtained as two versions of coinvariants functors defined by Hausser-Nill and by Bulacu-Caenepeel respectively.. The purpose of this thesis is to study the tensor functors and their right adjoints in various cases. In all cases, we obtain the right adjoints as a Hom-functor by choosing suitable units and counits. As one of the main results of this thesis, we show that the Hom-functor is right adjoint to the comparison functor. Thus, this Hom-functor is functorially isomorphic to the Hausser-Nill coinvariants functor defined by Hausser-Nill and also to the Bulacu-Caenepeel coinvariants functor . Our approach leads to a new description of the concept of coinvariants in terms of Hom-functor and provides alternative techniques to handle modules over quasi-Hopf algebras. For an H-comodule algebra A, we consider the category of two-sided Hopf modules and a generalized version of the comparison functor and introduce a Hom-functor as right adjoint to this comparison functor. For this, we donot need any quasi-antipode. In case H is a quasi-Hopf algebra, we consider generalised versions of the coinvariants and state the Fundamental Theorems for category two-sided Hopf modules. We show that this Hom-functor is isomorphic to both generalized version of coinvariants. In the special case A = H, we obtain the isomorphisms between the Hom-functor and the original coinvariant functors.
Lizenz:	Urheberrechtsschutz
Fachbereich / Einrichtung:	Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Algebra und Zahlentheorie
Dokument erstellt am:	05.11.2008
Dateien geändert am:	05.11.2008
Promotionsantrag am:	18.07.2008
Datum der Promotion:	30.10.2008