On Hopf algebras with triangular decomposition

Abstract

In this survey, we first review some known results on the representationtheory of algebras with triangular decomposition, including the classification of the simple modules. We then discuss a recipe to construct Hopf algebras with triangular decomposition. Finally, we extend to these Hopf algebras the main results of a previous work of the author regarding projective modules over Drinfeld doubles of bosonizations of Nichols algebras and groups.