On Auslander-Reiten Components of Blocks and Self-Injective Biserial Algebras

DOI10.2307/2154159zbMath0757.16004OpenAlexW4235489098MaRDI QIDQ4000828

Karin Erdmann, Andrzej Skowroński

Publication date: 26 September 1992

Full work available at URL: https://doi.org/10.2307/2154159

zbMATH Keywords

Auslander-Reiten componentspolynomial growthdefect groupsblockgroup algebraself-injective algebrastable Auslander-Reiten quiverbound quiverdihedral algebrasEuclidean componentrepresentation-infinite special biserial algebras

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Representations of orders, lattices, algebras over commutative rings (16G30) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Representations of quivers and partially ordered sets (16G20)

Related Items (44)

Derived equivalence classification of weakly symmetric algebras of Euclidean type. ⋮ On Auslander-Reiten Quivers of Enveloping Algebras of Restricted Lie Algebras ⋮ On the vertices of modules in the Auslander-Reiten quiver. II ⋮ Derived equivalence classification of Brauer graph algebras ⋮ Brauer graph algebras are closed under derived equivalence ⋮ Universal Galois coverings of self-injective algebras by repetitive algebras and Hochschild cohomology ⋮ Multiserial and special multiserial algebras and their representations ⋮ Auslander-Reiten components of symmetric special biserial algebras ⋮ Weighted surface algebras ⋮ Derived equivalence classification of one-parametric self-injective algebras. ⋮ A new parametrisation of tilting modules for \(\text{GL}(3,k)\) over characteristic 2. ⋮ On Auslander-Reiten components for group algebras ⋮ A finite dimensional algebra of the diagram of a knot ⋮ Brauer configuration algebras: a generalization of Brauer graph algebras ⋮ Selfinjective algebras with hereditary stable slice ⋮ Universal deformation rings of modules for generalized Brauer tree algebras of polynomial growth ⋮ On simple-minded systems and \(\tau \)-periodic modules of self-injective algebras ⋮ The Auslander-Reiten quiver of perfect complexes for a self-injective algebra ⋮ Support varieties, AR-components, and good filtrations. ⋮ Dessins d'enfants, Brauer graph algebras and Galois invariants ⋮ Hybrid algebras ⋮ Combinatorial restrictions on the tree class of the Auslander-Reiten quiver of a triangulated category ⋮ ALGEBRAS OF GENERALIZED DIHEDRAL TYPE ⋮ Auslander-Reiten theory of small half quantum groups ⋮ Algebras with cycle-finite Galois coverings ⋮ On support varieties of Auslander-Reiten components ⋮ Positive Galois coverings of self-injective algebras. ⋮ Universal deformation rings of modules for algebras of dihedral type of polynomial growth ⋮ Pure injective indecomposable modules over 1-domestic string algebras. ⋮ Galois actions and blocks of tame infinitesimal group schemes ⋮ On the stable module category of a self-injective algebra ⋮ Representation type of finite quiver Hecke algebras of type $D^{(2)}_{\ell +1}$ ⋮ Special multiserial algebras, Brauer configuration algebras and more: A survey ⋮ Polyhedral groups, McKay quivers, and the finite algebraic groups with tame principal blocks. ⋮ Trivial extensions of gentle algebras and Brauer graph algebras. ⋮ From Brauer graph algebras to biserial weighted surface algebras ⋮ Group-graded algebras, extensions of infinitesimal groups, and applications ⋮ Brauer Graph Algebras ⋮ Unnamed Item ⋮ Universal deformation rings of string modules over certain class of self-injective special biserial algebras ⋮ Socle deformations of selfinjective orbit algebras of tilted type ⋮ Weighted surface algebras: general version ⋮ Galois coverings of selfinjective algebras by repetitive algebras ⋮ Auslander-Reiten components for Lie algebras of reductive groups

Cites Work

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• Group algebras of polynomial growth
• The Auslander-Reiten quiver of a modular group algebra revisited
• Local methods in block theory
• Tame algebras and integral quadratic forms
• Module correspondence in Auslander-Reiten quivers for finite groups
• Modular representation theory: New trends and methods
• Tame biserial algebras
• Iterated tilted algebras of type \({\tilde {\mathbb A}}_ n\)
• On the Auslander-Reiten quiver of a finite group
• Galois coverings of representation-infinite algebras
• Modules of bounded length in Auslander-Reiten components
• Selfinjective algebras of polynomial growth
• The construction of almost split sequences. III: Modules over two classes of tame local algebras
• Algebren, Darstellungsköcher, Überlagerungen und zurück
• Representations, resolutions and Quillen's dimension theorem
• Covering spaces in representation-theory
• Selfinjective biserial standard algebras
• Blocks of tame representation type and related algebras
• The dimensions of periodic modules over modular group algebras
• Domestic trivial extensions of simply connected algebras
• Algebras with cycle-finite derived categories
• Algebras and Dihedral Defect Groups
• Auslander-reiten sequences with few middle terms and applications to string algebrass
• On Tame Algebras and Bocses
• Representation theory of artin algebras VI: A functorial approach to aimost split sequences
• Trivial Extensions of Tilted Algebras
• The Structure of Stable Components
• Functorial Filtrations III: Semidihedral Algebras
• The Auslander-Reiten quiver of a finite group
• The Auslander-Reiten quiver of a finite group

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