We introduce the notions of a D-standard abelian category and a K-standard additive category. We prove that for a finite dimensional algebra A, its module category is D-standard if and only if any derived autoequivalence on Ais standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. We prove that if the subcategory of projective A-modules is K-standard, then the module category is D-standard. We provide new examples of D-standard module categories.
@inproceedings{chen,2018,,
title={, The D-standard and K-standard categories,},
author={Chen, Xiao-Wu, and Ye, Yu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190319211614497829208},
booktitle={Adv. Math.},
year={2018},
}
Chen, Xiao-Wu, and Ye, Yu. , The D-standard and K-standard categories,. 2018. In Adv. Math.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190319211614497829208.