The Hall algebra of cyclic serial algebra
type: Item
instance of: scholarly article
title: The Hall algebra of cyclic serial algebra
zbMATH Open document ID: 0839.16011
published in: Science in China. Series A
publication date: 1996-06-18T00:00:00Z
review text: The study of Hall algebras is strongly related to the study of quantum groups. In this paper, the author obtains some results for Hall algebras of a cyclic serial algebra which are similar to those of Hall algebras of representation directed algebras. Namely, let \(R\) be a finite cyclic algebra with \(n\) simples and such that all the indecomposable projective modules have length \(m\). The author introduces two orders \(\prec_1\) and \(\prec_2\) in \((\mathbb{Z}^+)^{nm}\) and through a one-to-one correspondence these orders can be regarded as orders on the isoclasses of finite \(R\)-modules. He proves then that a Hall algebra of a cyclic serial algebra can be identified with its Loewy subalgebra and its rational extension has a basis similar to the basis of Poincaré-Birkhoff-Witt type.
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 700530
zbMATH Keywords: filtered rings
zbMATH Keywords: intended skew polynomial rings
zbMATH Keywords: Hall algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: representation directed algebras
zbMATH Keywords: finite cyclic algebras
zbMATH Keywords: indecomposable projective modules
zbMATH Keywords: Loewy subalgebra
zbMATH Keywords: basis of Poincaré-Birkhoff-Witt type
author: Jin Yun Guo
reviewed by: Flávio U. Coelho
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 700530