The strong global dimension of piecewise hereditary algebras
Résumé
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.
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