The triangulated hull of periodic complexes

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.

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Received 13 April 2016

Accepted 26 August 2016

Published 4 June 2018