Clasifications of t-structures in the derived category of the Kronecker Algebra

Abstract

We study suspended subcategories of the bounded derived category Db(mod H), where H is a tame hereditary k-algebra. First, we consider U_M the smallest suspended subcategory containing M, where Mis a brick.We give necessary and sufficient conditions for U_M to be an aisle and we show that it occurs when M is a silting object. Then we concentrate on the case that H is the path algebra of the Kronecker quiver. In that context, we classify all the suspended subcategories having Ext-projective objects. We prove that these are aisles and we give their description. Finally, we determine which suspended subcategories generated by an object are aisles and we describe them.