The strong global dimension of piecewise hereditary algebras

Edson Ribeiro Alvares (1) , Patrick Le Meur (2) , Eduardo N. Marcos (3)

1 DM - UFPR - Departamento de Matematica - Universidade Federal do Parana
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 IME

Let T be a tilting object in a triangulated category which is equivalent to the bounded derived category of a finite-dimensional hereditary algebra. The text investigages the strong global dimension, in the sense of Ringel, of the opposite algebra A of the endomorphism algebra of T. This invariant is expressed in terms of the lengths of the sequences of tilting objects with last term equal to T, such that each term arises from the preceding one by a tilting mutation, and such that the opposite of the endomorphism algebra of the first term is a tilted algebra. It is also expressed in terms on the hereditary abelian subcategories of the triangulated category.

Mots clés: piecewise hereditary algebra; strong global dimension; triangulated category; derived category; tilting; tilting mutation

Domaines: Théorie des représentations [math.RT]

Edson Ribeiro Alvares, Patrick Le Meur, Eduardo N. Marcos. The strong global dimension of piecewise hereditary algebras. 2013. ⟨hal-00825031v1⟩