A homological characterization of piecewise hereditary algebras.

DOI10.1007/s00209-007-0268-3zbMath1193.16005OpenAlexW2080422984MaRDI QIDQ938271

Dieter Happel, Dan Zacharia

Publication date: 18 August 2008

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-007-0268-3

zbMATH Keywords

pathsfinite-dimensional algebrasderived categoriestriangulated categoriespiecewise hereditary algebrasstrong global dimensionindecomposable objects

Mathematics Subject Classification ID

Related Items (31)

String and band complexes over string almost gentle algebras ⋮ On compact exceptional objects in derived module categories ⋮ A class of simple Lie algebras attached to unit forms ⋮ FINITISTIC DIMENSIONS AND PIECEWISE HEREDITARY PROPERTY OF SKEW GROUP ALGEBRAS ⋮ Differential modules over quadratic monomial algebras ⋮ Some examples of \(t\)-structures for finite-dimensional algebras ⋮ Nakayama algebras and Fuchsian singularities ⋮ On the braid group action on exceptional sequences for weighted projective lines ⋮ Irreducible morphisms in the bounded derived category via the category of complexes of fixed size ⋮ Piecewise hereditary Nakayama algebras. ⋮ Algebra extensions and derived-discrete algebras ⋮ Sections in the bounded derived category of piecewise hereditary algebras ⋮ Jordan-Hölder theorems for derived module categories of piecewise hereditary algebras. ⋮ HOMOLOGICAL DIMENSIONS OF CROSSED PRODUCTS ⋮ Hereditary categories with Serre duality which are generated by preprojectives ⋮ Strong global dimension of commutative rings and schemes ⋮ Hereditary triangulated categories ⋮ Topological invariants of piecewise hereditary algebras ⋮ $(m,n)$-Quasitilted and $(m,n)$-almost hereditary algebras ⋮ Morphisms in the infinite radical of the bounded derived category ⋮ Brauer-Thrall type theorems for derived module categories ⋮ The strong global dimension of piecewise hereditary algebras ⋮ Hereditary uniserial categories with Serre duality ⋮ Derived Brauer–Thrall Type Theorem I for Artin Algebras ⋮ Homological properties of piecewise hereditary algebras. ⋮ Numerically finite hereditary categories with Serre duality ⋮ On the type of a category of complexes of fixed size and the strong global dimension ⋮ On non-homogeneous tubes and components of type \(\mathbb{Z}A_{\infty}\) in the bounded derived category ⋮ Strong global dimensions of triangulated categories with respect to silting objects ⋮ Piecewise hereditary incidence algebras ⋮ Piecewise hereditary algebras under field extensions

Cites Work

• Bricks in hereditary length categories
• Tame algebras and integral quadratic forms
• Finiteness of the strong global dimension of radical square zero algebras.
• Algebras with cycle-finite derived categories
• Hereditary abelian categories with tilting object over arbitrary base fields
• Piecewise hereditary algebras
• Bounded derived categories and repetitive algebras.
• Tilting in abelian categories and quasitilted algebras
• A characterization of hereditary categories with tilting object
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