arXiv subjects
Publications and source records attributed to Fabio Stumbo.
In this paper we investigate a family of algebras endowed with a suitable non-degenerate bilinear form that can be used to define two different notions of dual for a given right ideal. We apply our results to the classification of the right ideals and their duals in the cyclic group algebra, in the Taft algebra and in another example of Hopf algebra arising as bosonization.
In this paper, the notion of universal enveloping algebra introduced in [A. Ardizzoni, \emph{A First Sight Towards Primitively Generated Connected Braided Bialgebras}, submitted. (arXiv:0805.3391v3)] is specialized to the case of braided vector spaces whose Nichols algebra is quadratic as an algebra. In this setting a classification of universal enveloping algebras for braided vector spaces of dimension not greater than 2 is handled. As an application, we investigate the structure of primitively generated connected braided bialgebras whose braided vector space of primitive elements forms a Nichols algebra which is quadratic algebra.