Sur quelques propriétés des algèbres de Hopf

Abstract : In this work, we study somes properties of Hopf algebras and of their modules. First we expose the works of Radford, Nichols and Zoeller on the freeness of Hopf algebras, and we show that a connected graded Hopf algebra is free over its Hopf subalgebras. Second we show that if a graded connected Hopf algebra over a commutative field of characteristic 0, where all homogenous elements of strictly positive degree are nilpotents, then it's commutative and cocommutative, hence it's the exterior algebra over the primitive elements, which generalise a result of Hopf without commutativity in finite dimension. In the end, we generalise the results of J Bergen, we give conditions implying that the spaces of invariants associated to a differents Hopf subalgebras are distincts
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Mustapha Ameur. Sur quelques propriétés des algèbres de Hopf. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1996. Français. ⟨NNT : 1996METZ023S⟩. ⟨tel-01777135⟩

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