Grothendieck groups and Auslander-Reiten \((d + 2)\)-angles

DOI10.1016/J.JALGEBRA.2020.09.048zbMath1476.16014arXiv1912.11397OpenAlexW3094803106WikidataQ112881743 ScholiaQ112881743MaRDI QIDQ2215797

Panyue Zhou

Publication date: 14 December 2020

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

Full work available at URL: https://arxiv.org/abs/1912.11397

zbMATH Keywords

Grothendieck groupslocally finite categoriesgeneralized Auslander-Reiten trianglesgeneralized triangulated categories

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Grothendieck groups, (K)-theory and commutative rings (13D15) Derived categories, triangulated categories (18G80)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(n\)-abelian and \(n\)-exact categories
• The axioms for \(n\)-angulated categories
• The Grothendieck group of an \(n\)-angulated category
• Auslander-Reiten \((d + 2)\)-angles in subcategories and a \((d + 2)\)-angulated generalisation of a theorem by Brüning
• Auslander-Reiten triangles, Ziegler spectra and Gorenstein rings
• Relations for the Grothendieck groups of triangulated categories
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Noetherian hereditary abelian categories satisfying Serre duality
• Relations for Grothendieck Groups of Artin Algebras
• Representation theory of artin algebras iii almost split sequences
• Representation theory of artin algebras IV¹⁾Invariants given by almost split sequences
• n-angulated categories
• The morphism axiom for n-angulated categories

This page was built for publication: Grothendieck groups and Auslander-Reiten \((d + 2)\)-angles