Categorical Webs and S-Duality in 4d $${\mathcal {N}}$$N = 2 QFT
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03461-0
Abstract: We review the categorical approach to the BPS sector of a 4d $$\mathcal {N}=2$$N=2 QFT, clarifying many tricky issues and presenting a few novel results. To a given $$\mathcal {N}=2$$N=2 QFT one associates several triangulated… read more here.
Keywords: mathcal qft; qft; categorical webs; webs duality ... See more keywords
Symmetry of the Definition of Degeneration in Triangulated Categories
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DOI: 10.1007/s10468-018-9799-z
Abstract: Module structures of an algebra on a fixed finite dimensional vector space form an algebraic variety. Isomorphism classes correspond to orbits of the action of an algebraic group on this variety and a module is… read more here.
Keywords: definition; symmetry definition; definition degeneration; degeneration triangulated ... See more keywords
Abelian Categories from Triangulated Categories via Nakaoka–Palu’s Localization
Sign Up to like & getrecommendations! Published in 2022 at "Applied Categorical Structures"
DOI: 10.1007/s10485-021-09668-4
Abstract: The aim of this paper is to provide an expansion of Abe–Nakaoka’s heart construction to the following two different realizations of the module category over the endomorphism ring of a rigid object in a triangulated… read more here.
Keywords: categories triangulated; localization; nakaoka palu; categories via ... 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
One-sided triangulated categories induced by concentric twin cotorsion pairs
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DOI: 10.1142/s021949882050142x
Abstract: Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. Nakaoka and Palu introduced the notion of concentric twin cotorsion pairs in extriangulated categories. In this paper,… read more here.
Keywords: concentric twin; twin cotorsion; triangulated categories; cotorsion pairs ... See more keywords
Proper resolutions and Gorensteinness in triangulated categories
Sign Up to like & getrecommendations! Published in 2017 at "Rocky Mountain Journal of Mathematics"
DOI: 10.1216/rmj-2017-47-3-1013
Abstract: Let T be a triangulated category with triangulation ∆, ξ ⊆ ∆ a proper class of triangles and C an additive full subcategory of T . We provide a method for constructing a proper C(ξ)-resolution… read more here.
Keywords: class triangles; triangulated categories; homological algebra; mathematics ... See more keywords