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Mathematics > Representation Theory

Title: Iyama-Solberg correspondence for exact dg categories

Authors: Xiaofa Chen
Abstract: We generalize the notions of $d$-cluster tilting pair and $d$-Auslander exact dg category to $d$-precluster tilting triple and $d$-minimal Auslander--Gorenstein exact dg category. We give a bijection between equivalence classes of $d$-precluster tilting triples and equivalence classes of $d$-minimal Auslander--Gorenstein exact dg categories. Our bijection generalizes Iyama--Solberg correspondence for module categories.
Comments: v2, a subsection on an equivalence of $\infty$-groupoids is added. Comments are very welcome!
Subjects: Representation Theory (math.RT); Category Theory (math.CT)
Cite as: arXiv:2401.02064 [math.RT]
  (or arXiv:2401.02064v2 [math.RT] for this version)

Submission history

From: Xiaofa Chen [view email]
[v1] Thu, 4 Jan 2024 05:02:45 GMT (26kb,D)
[v2] Fri, 9 Feb 2024 09:18:52 GMT (30kb,D)

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