Stephen Zito
Published 2016-08-04Version 1
We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. We investigate how various properties of a C-module are affected when considered in the module category of B. We give a complete classification of the projective dimension of a C-module inside the module category of B. If a C-module M is rigid, we show two sufficient conditions for M to be a rigid B-module. In particular, if M is an indecomposable and rigid C-module, we prove M is always a rigid B-module.
Comments: 20 pages. arXiv admin note: text overlap with arXiv:1410.1732, arXiv:1604.06907 by other authors
From triangulated categories to module categories via localisation
$n$-cluster tilting subcategories from gluing systems of representation-directed algebras
The bounded derived category of a poset
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