The strong global dimension of piecewise hereditary algebras

Edson Ribeiro Alvares (1) , Patrick Le Meur (2, 3) , Eduardo N. Marcos (4)

1 DM - UFPR - Departamento de Matematica - Universidade Federal do Parana
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
4 IME

Let T be a tilting object in a triangulated category equivalent to the bounded derived category of a hereditary abelian category with finite dimensional homomorphism spaces and split idempotents. This text investigates the strong global dimension, in the sense of Ringel, of the endomorphism algebra of T. This invariant is expressed using the infimum of the lengths of the sequences of tilting objects successively related by tilting mutations and where the last term is T and the endomorphism algebra of the first term is quasi-tilted. It is also expressed in terms of the hereditary abelian generating subcategories of the triangulated category.

Mots clés: derived category; representation theory; finite-dimensional algebras; tilting; tilting mutation; piecewise hereditary algebra; strong global dimension; triangulated category

Domaines: Théorie des représentations [math.RT]

Edson Ribeiro Alvares, Patrick Le Meur, Eduardo N. Marcos. The strong global dimension of piecewise hereditary algebras. Journal of Pure and Applied Algebra, 2017, 481, pp.36-67. ⟨10.1016/j.jalgebra.2017.02.012⟩. ⟨hal-00825031v3⟩