The algebras with discrete derived category.

DOI10.1006/jabr.2001.8783zbMath1038.16010OpenAlexW2062046146MaRDI QIDQ5949417

Dieter Vossieck

Publication date: 30 March 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.8783

zbMATH Keywords

finite-dimensional algebrasderived categories of bounded complexesindecomposable complexesrepetitive algebras

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10)

Related Items (62)

\(m\)-cluster tilted algebras of Euclidean type ⋮ Jordan-Hölder theorems for derived categories of derived discrete algebras ⋮ A note on generic objects and locally finite triangulated categories ⋮ On the coefficients of the Coxeter polynomial of an accessible algebra. ⋮ Spherical subcategories in representation theory ⋮ Derived Categories of Schur Algebras ⋮ Morphisms between indecomposable complexes in the bounded derived category of a gentle algebra ⋮ Derived equivalences for hereditary Artin algebras ⋮ Derived representation type and field extensions ⋮ Derived representation type and cleaving functors ⋮ The Ziegler spectrum for derived-discrete algebras ⋮ Derived equivalence classification of the gentle two-cycle algebras ⋮ Finite and bounded Auslander-Reiten components in the derived category. ⋮ The almost split triangles for perfect complexes over gentle algebras. ⋮ One-point extensions and derived equivalence. ⋮ Complete gentle and special biserial algebras are \(g\)-tame ⋮ Indecomposables with smaller cohomological length in the derived category of gentle algebras ⋮ On algebras of strongly derived unbounded type. ⋮ The derived-discrete algebras over the real numbers ⋮ Classifying recollements of derived module categories for derived discrete algebras ⋮ Eventually homological isomorphisms in recollements of derived categories ⋮ Derived Hall algebras of one-cycle gentle algebras: the infinite global dimension case ⋮ Rigid divisors on surfaces ⋮ Algebra extensions and derived-discrete algebras ⋮ On riedtmann’s Lie algebra of the gentle one-cycle algebra Λ(n−1,1,1) ⋮ A geometric realization of silting theory for gentle algebras ⋮ Discrete triangulated categories ⋮ Singular equivalences and Auslander-Reiten conjecture ⋮ Exceptional cycles for perfect complexes over gentle algebras ⋮ The relative singularity category of a non-commutative resolution of singularities ⋮ Exceptional sequences in the derived category of a gentle algebra ⋮ Singularity categories of representations of algebras over local rings ⋮ Classification of discrete derived categories ⋮ The graded centers of derived discrete algebras. ⋮ On the representation type of subcategories of derived categories ⋮ The derived-discrete algebras and standard equivalences ⋮ Weighted locally gentle quivers and Cartan matrices. ⋮ Combinatorial derived invariants for gentle algebras. ⋮ SHOD STRING ALGEBRAS ⋮ The equivalence of two notions of discreteness of triangulated categories ⋮ On Extensions for Gentle Algebras ⋮ Discrete derived categories. I: Homomorphisms, autoequivalences and t-structures ⋮ Derived categories of graded gentle one-cycle algebras ⋮ Brauer-Thrall type theorems for derived module categories ⋮ ON THE EXISTENCE OF A DERIVED EQUIVALENCE BETWEEN A KOSZUL ALGEBRA AND ITS YONEDA ALGEBRA ⋮ The Krull-Gabriel dimension of discrete derived categories ⋮ Derived Brauer–Thrall Type Theorem I for Artin Algebras ⋮ Singularity categories of Gorenstein monomial algebras ⋮ Contractible stability spaces and faithful braid group actions ⋮ Thick subcategories of discrete derived categories ⋮ On the type of a category of complexes of fixed size and the strong global dimension ⋮ Discrete derived categories II: the silting pairs CW complex and the stability manifold ⋮ Derived tame Nakayama algebras ⋮ Algebras whose Coxeter polynomials are products of cyclotomic polynomials. ⋮ On derived unique gentle algebras ⋮ COHOMOLOGICAL LENGTH FUNCTIONS ⋮ Some new categorical invariants ⋮ Brauer Graph Algebras ⋮ Algebras of acyclic cluster type: Tree type and typeà ⋮ Derived tame local and two-point algebras. ⋮ On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras ⋮ Generically Trivial Derived Categories

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• The standard form of a representation-finite algebra
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• Generalized tilted algebras of type a_n
• Trivial Extensions of Tilted Algebras
• Auslander-Reiten Triangles in Derived Categories of Finite-Dimensional Algebras

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