• Lifting to two-term relative maximal rigid subcategories in triangulated categories

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0053

• # Keywords

Tilting subcategories; maximal rigid objects; cluster tilting objects.

• # Abstract

Let $\mathscr{C}$ be a triangulated category with shift functor [1] and $\mathscr{R}$ a contravariantly rigid subcategory of $\mathscr{C}$ . We show that a tilting subcategory of $\mod\mathscr{ R}$ lifts to a two-term maximal $\mathscr{R}$[1]-rigid subcategory of $\mathscr{C}$ . As an application, our result generalizes a result by Xie and Liu (Proc. Amer. Math. Soc. 141(10) (2013) 3361–3367) for maximal rigid objects and a result by Fu and Liu (Comm. Algebra 37(7) (2009) 2410–2418) for cluster tilting objects.

• # Author Affiliations

1. College of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, Hunan, People’s Republic of China

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019