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Abstract
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For a triangulated category
with
a cluster tilting subcategory
which contains infinitely many indecomposable objects, the notion of weak
-cluster tilting subcategories
of
is introduced. We use them
to study the
-tilting theory
in the module category over
.
Inspired by the work of Iyama, Jørgensen and Yang (2014), we introduce the notion of
-tilting subcategories
of mod
,
and show that there exists a bijection between weak
-cluster tilting
subcategories of
and support
-tilting
subcategories of mod
.
Moreover, we describe the subcategories of mod
which correspond to cluster tilting subcategories of
. This
generalizes and improves results by Adachi, Iyama and Reiten (2014), Beligiannis
(2013), and Yang and Zhu (2019).
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Dedicated to Professor Idun Reiten on
the occasion of her 76th birthday
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Keywords
ghost cluster tilting subcategories, (support)
$\tau$-tilting subcategories, tilting subcategories,
cluster tilting subcategories
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Mathematical Subject Classification 2010
Primary: 16G20, 18E30
Secondary: 16G99, 16G70
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Milestones
Received: 25 February 2018
Revised: 16 January 2019
Accepted: 18 January 2019
Published: 24 October 2019
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