The strong global dimension of piecewise hereditary algebras
| Autor: | Alvares, Edson Ribeiro, Meur, Patrick Le, Marcos, Eduardo N. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Journal of Algebra 481 (2017), 36-67 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2017.02.012 |
| Popis: | 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. Comment: Final published version. After refereeing, historical considerations were added and the length of the article was reduced: Introduction and Section 1 were reformulated; Subsection 2.1 was moved to Section 1 (with an abridged proof); Subsection 3.2 was reformulated (with an abridged proof); The proof in A.5 was rewritten (now shorter); And minor rewording was processed throughout the article |
| Databáze: | arXiv |
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