Split t-structures and torsion pairs in the derived category of a hereditary algebra

ASSEM IBRAHIM; SOUTO SALORIO, MARIA JOSE; TREPODE, SONIA

Buenos Aires

Congreso; XXI Coloquio Latinoamericano de Algebra; 2016

Universidad de Buenos Aires

We give necessary and sucient conditions for torsion pairs in a hereditarycategory to be in bijection with t-structures in the bounded derived category of thathereditary category. We prove that the existence of a split t-structure with nontrivial heartin a semiconnected Krull-Schmidt category implies that this category is equivalent to thederived category of a hereditary category. We construct a bijection between split torsionpairs in the module category of a tilted algebra having a complete slice in the preinjectivecomponent with corresponding t-structures. Finally, we classify split t-structures in thederived category of a hereditary algebra.