2021 Fiscal Year Research-status Report

Cluster theory through derived categories and self-injective algebras

Research Project

Project/Area Number	18K03238
Research Institution	Nagoya University
Principal Investigator	ダルポエリック名古屋大学, 多元数理科学研究科(国際), 准教授 (00785959)
Project Period (FY)	2018-04-01 – 2023-03-31
Keywords	Fractionally Calabi-Yau / self-injective algebra / periodic / projective resolution
Outline of Annual Research Achievements	This year, we have extended earlier results characterising periodicity in trivial extension algebras to more general classes of finite-dimensional self-injective algebras. The principal result characterises periodicity and twisted periodicity of a self-injective orbit algebra in terms of the (twisted) fractionally Calabi-Yau property of the associated algebra of finite global dimension.
Current Status of Research Progress	Current Status of Research Progress 2: Research has progressed on the whole more than it was originally planned. Reason The result obtained are in line with the expectations.
Strategy for Future Research Activity	I plan to study mutation theory of d-silting objects of derived categories, in particular how it relates to mutation of cluster-tilting subcategories.
Causes of Carryover	The grant will be used for attending one or two international conferences and international research visits, and for buying books and other equipment.

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