nZ-Gorenstein cluster tilting subcategories
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DOI: 10.1016/j.jalgebra.2021.04.004
Abstract: Abstract Let Λ be an Artin algebra. In this paper, the notion of n Z -Gorenstein cluster tilting subcategories will be introduced. It is shown that every n Z -cluster tilting subcategory of mod-Λ is… read more here.
Keywords: gorenstein cluster; cluster; tilting subcategory; tilting subcategories ... See more keywords
GROTHENDIECK GROUPS OF TRIANGULATED CATEGORIES VIA CLUSTER TILTING SUBCATEGORIES
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DOI: 10.1017/nmj.2020.12
Abstract: Let $k$ be a field, and let ${\mathcal{C}}$ be a $k$-linear, Hom-finite triangulated category with split idempotents. In this paper, we show that under suitable circumstances, the Grothendieck group of ${\mathcal{C}}$, denoted by $K_{0}({\mathcal{C}})$, can… read more here.
Keywords: cluster tilting; grothendieck groups; groups triangulated; triangulated categories ... See more keywords
On cluster-tilting objects in a triangulated category with Serre duality
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DOI: 10.1080/00927872.2016.1214273
Abstract: ABSTRACT Let ???? be a Krull–Schmidt, Hom-finite triangulated category with a Serre functor and a cluster-tilting object T. We introduce the notion of an FΛ-stable support τ-tilting module, induced by the shift functor and the… read more here.
Keywords: tilting objects; cluster tilting; category serre; triangulated category ... See more keywords