Mathematical Research Letters

Volume 25 (2018)

Number 1

The triangulated hull of periodic complexes

Pages: 199 – 236



Torkil Stai (Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), Trondheim, Norway)


In the terms of a ‘periodic derived category’, we describe explicitly how the orbit category of the bounded derived category of an algebra with respect to a power of the shift functor embeds in its triangulated hull. We obtain a large class of algebras whose orbit categories are strictly smaller than their triangulated hulls and a realization of the phenomenon that an automorphism need not induce the identity functor on the associated orbit category.

Received 13 April 2016

Accepted 26 August 2016

Published 4 June 2018