Higman ideal, stable Hochschild homology and Auslander-Reiten conjecture.

DOI10.1007/s00209-010-0825-zzbMath1261.16010OpenAlexW2026141306WikidataQ123218833 ScholiaQ123218833MaRDI QIDQ415476

Yuming Liu, Alexander Zimmermann, Guodong Zhou

Publication date: 8 May 2012

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

Full work available at URL: https://doi.org/10.1007/s00209-010-0825-z

zbMATH Keywords

finite dimensional algebrassimple modulesstable equivalences of Morita typestable module categoriesAuslander-Reiten conjecturetransfer mapsHigman idealsprojective centerstable Hochschild homology

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Representations of associative Artinian rings (16G10)

Related Items

Külshammer ideals of algebras of quaternion type ⋮ Classification of Symmetric Special Biserial Algebras With At Most One Non-Uniserial Indecomposable Projective ⋮ The dg Leavitt algebra, singular Yoneda category and singularity category ⋮ ON GRADED SYMMETRIC CELLULAR ALGEBRAS ⋮ Deformed preprojective algebras of type \(L\): Külshammer spaces and derived equivalences. ⋮ Stable equivalences of Morita type do not preserve tensor products and trivial extensions of algebras ⋮ On a Question of Rickard on Tensor Products of Stably Equivalent Algebras ⋮ On singular equivalences of Morita type ⋮ Classifying tame blocks and related algebras up to stable equivalences of Morita type. ⋮ Morphism spaces in stable categories of Frobenius algebras ⋮ Transfer maps in Hochschild (co)homology and applications to stable and derived invariants and to the Auslander–Reiten conjecture ⋮ Integrals for finite tensor categories ⋮ Support variety theory is invariant under singular equivalences of Morita type ⋮ Auslander-Reiten conjecture for symmetric algebras of polynomial growth. ⋮ Tate-Hochschild cohomology for periodic algebras ⋮ Stable equivalences of Morita type and stable Hochschild cohomology rings. ⋮ Projective objects and the modified trace in factorisable finite tensor categories ⋮ Hochschild Homology Invariants of Külshammer Type of Derived Categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classifying tame blocks and related algebras up to stable equivalences of Morita type.
• Auslander-Reiten conjecture for symmetric algebras of polynomial growth.
• Gluing of idempotents, radical embeddings and two classes of stable equivalences.
• Generalized Reynolds ideals and derived equivalences for algebras of dihedral and semidihedral type.
• Calabi-Yau Frobenius algebras.
• Higman's criterion revisited.
• A remark on Higman's result about separable algebras
• Algebren, Darstellungsköcher, Überlagerungen und zurück
• Cartan matrices and Grothendieck groups of stable categories
• Blocks of tame representation type and related algebras
• Invariance and localization for cyclic homology of DG algebras
• Derived equivalences for group rings
• Derived categories and stable equivalence
• Stable equivalences of Morita type for self-injective algebras and \(p\)-groups
• Generalized Reynolds ideals for non-symmetric algebras.
• Nilpotente Elemente in Ringen von endlicher globaler Dimension
• Lattices over orders I
• Constructions of stable equivalences of Morita type for finite dimensional algebras. II.
• Central ideals and Cartan invariants of symmetric algebras.
• The stable group of a selfinjective nakayama algebra
• Construction of stable equivalences of Morita type for finite-dimensional algebras I
• On stable equivalences induced by exact functors
• Summands of Stable Equivalences of Morita Type
• The stable equivalence for algebras of finite representation type
• Algebras stably equivalent to selfinjective special biserial algebras
• Derived Equivalences As Derived Functors
• A note on the stable equivalence conjecture
• Transfer maps in Hochschild (co)homology and applications to stable and derived invariants and to the Auslander–Reiten conjecture
• Constructions of stable equivalences of Morita type for finite-dimensional algebras III
• Stable equivalences of adjoint type
• Invariance of Generalised Reynolds Ideals Under Derived Equivalences
• On Orders In Separable Algebras
• Invariance of Hochschild cohomology algebras under stable equivalences of Morita type.