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The D-standard and K-standard categories

Authors :
Xiao-Wu Chen
Yu Ye
Source :
Advances in Mathematics. 333:159-193
Publication Year :
2018
Publisher :
Elsevier BV, 2018.

Abstract

We introduce the notions of a $\mathbf{D}$-standard abelian category and a $\mathbf{K}$-standard additive category. We prove that for a finite dimensional algebra $A$, its module category is $\mathbf{D}$-standard if and only if any derived autoequivalence on $A$ is standard, that is, given by a two-sided tilting complex. We prove that if the subcategory of projective $A$-modules is $\mathbf{K}$-standard, then the module category is $\mathbf{D}$-standard. We provide new examples of $\mathbf{D}$-standard module categories.<br />revised, comments are welcome

Details

ISSN :
00018708
Volume :
333
Database :
OpenAIRE
Journal :
Advances in Mathematics
Accession number :
edsair.doi.dedup.....5d433a687aa7a66ec293d8882277c1a5