Higher-dimensional orders, graph-orders, and derived equivalences
type: Item
instance of: scholarly article
title: Higher-dimensional orders, graph-orders, and derived equivalences
zbMATH Open document ID: 0973.16013
DOI: 10.1016/S0022-4049(99)90107-X
author: Michael Kauer
author: Klaus W. Roggenkamp
published in: Journal of Pure and Applied Algebra
publication date: 2001-11-25T00:00:00Z
review text: In an earlier paper Roggenkamp defined and studied a class of classical orders, which he called Green orders. These are \(p\)-adic analogues for Brauer tree algebras, and indeed, blocks of finite group rings over a complete discrete valuation ring of characteristic 0 with residue field of characteristic \(p\) turn out to be Green orders. In the present paper the authors generalize the construction of Green orders in two directions. They generalize to coefficient domains being commutative complete regular local Noetherian rings of finite dimension. Moreover they allow more general (finite) graphs instead of trees as underlying combinatorial structure. The authors characterize these orders in intrinsic terms. The proof follows the line of the corresponding proof for Green orders. Moreover, the authors classify these orders up to derived equivalence. The result is more subtle than the corresponding result for Green orders. As a byproduct the authors manage to distinguish the derived equivalence class of two tame algebras of dihedral type which was left open in an earlier classification given by Thorsten Holm.
reviewed by: Alexander Zimmermann
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16G60
zbMATH DE Number: 1563012
zbMATH Keywords: classical orders
zbMATH Keywords: Green orders
zbMATH Keywords: Brauer tree algebras
zbMATH Keywords: derived equivalences
zbMATH Keywords: tame algebras of dihedral type
MaRDI profile type: Publication
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full work available at URL: s0022-4049(99)90107-x
OpenAlex ID: W2090853086
description: scientific article; zbMATH DE number 1563012