On two Hall algebra approaches to odd periodic triangulated categories
type: Item
instance of: scholarly article
title: On two Hall algebra approaches to odd periodic triangulated categories
zbMATH Open document ID: 1390.18027
author: Jie Sheng
author: Xueqing Chen
author: Fan Xu
published in: Science China. Mathematics
publication date: 2018-03-16T00:00:00Z
review text: The Hall algebra was firstly introduced by Steinitz around 1901 in the study of abelian \(p\)-groups. At the beginning, Hall algebras were closely related to the algebra of partitions and symmetric functions. The importance of Hall algebras introduced by Steinitz E.\ around 1901 has been highly recognized ever since the ground-breaking discovery of \textit{C. M. Ringel} [Invent. Math. 101, No. 3, 583--591 (1990; Zbl 0735.16009)]. Generally, the Hall algebra is a tool to encode the extension structure of a finitary category. Given an odd-periodic algebraic triangulated category, the authors compare Bridgeland's Hall algebra in the sense of \textit{T. Bridgeland} [Ann. Math. (2) 177, No. 2, 739--759 (2013; Zbl 1268.16017)] and the derived Hall algebra in the sense of \textit{B. Toën} [Duke Math. J. 135, No. 3, 587--615 (2006; Zbl 1117.18011)], \textit{J. Xiao} and \textit{F. Xu} [Duke Math. J. 143, No. 2, 357--373 (2008; Zbl 1168.18006)], and \textit{F. Xu} and \textit{X. Chen} [Algebr. Represent. Theory 16, No. 3, 673--687 (2013; Zbl 1275.16018)]. Then, it is shown that the former one is the twisted form of the tensor product of the latter one and a suitable group algebra.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16S30
zbMATH DE Number: 6851074
zbMATH Keywords: Hall algebra
zbMATH Keywords: derived Hall algebra
zbMATH Keywords: odd-periodic triangulated category
MaRDI profile type: Publication
full work available at URL: s11425-016-9129-4
OpenAlex ID: W2756323732
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DOI: 10.1007/S11425-016-9129-4
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description: scientific article; zbMATH DE number 6851074