Induced torsion structures on triangulated categories

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400052
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka Prefecture University
• Principal Investigator: Kato Kiriko 大阪府立大学, 理学(系)研究科(研究院), 准教授 (00347478)
• Research Collaborator: Jorgensen P. Newcastle大学, 数学統計科, 教授 ; Christensen L. W. Texas工科大学, 数学統計科, 教授 ; NAKAOKA Hiroyuki 鹿児島大学, 理学部, 准教授 ; IIMA Kei-ichiro 国立奈良高専, 一般科, 准教授 ; ENOMOTO Haruhisa ; NAKAMURA Tsutomu ; MATSUI Hiroki ; OGAWA Yasuaki ; KUBO Yuki ; HIRAYAMA Yukio
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 環論 / ホモロジー代数 / 圏論

Outline of Final Research Achievements

If a triangulated category has a torsion pair, then it is a category of extensions of subcategories. Decomposition into subcategories makes analysis simpler. Sometimes existence of torsion pairs may characterize categories. Our results consist mainly of two points: (1) We studied generalized torsion pairs with milder condition on orthogonality. We showed that they correspond with torsion pairs of quotient categories. (2) We are interested in categories of N-complexes since it has N-gons of recollements which is multiplied and recursive recollements. As a consequence, we showed that a derived category of N-complexes over a ring is triangle equivalent to that of ordinary (2-)complexes of upper triangular matrix rings over the ring.

Free Research Field

代数学