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Tilting subcategories; maximal rigid objects; cluster tilting objects.

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.

PANYUE ZHOU¹

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

Published

8 September 2020

Final version published online

8 September 2020