Semibricks and wide subcategories in extended module categories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908644254154752 |
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| author | Gupta, Esha Zhou, Yu |
| author_facet | Gupta, Esha Zhou, Yu |
| contents | For $d\geq 1$, we define semibricks and wide subcategories in the $d$-extended hearts of bounded $t$-structures on a triangulated category. We show that these semibricks are in bijection with finite-length wide subcategories. When the $d$-extended heart is the $d$-extended module category $d\mbox{-}\mathrm{mod}Λ$ of a finite-dimensional algebra $Λ$ over a field, we define left/right-finite semibricks and left/right-finite wide subcategories in $d\mbox{-}\mathrm{mod}Λ$ and show bijections with $(d+1)$-term simple-minded collections, generalising the bijections between $2$-term simple-minded collections, left/right-finite wide subcategories and left/right-finite semibricks in $\mathrm{mod}Λ$. We use a relation between semibricks and silting complexes to characterise which mutations of $(d+1)$-term silting complexes are again $(d+1)$-term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semibricks and wide subcategories in extended module categories Gupta, Esha Zhou, Yu Representation Theory Rings and Algebras 16G10, 16E35, 18G80 For $d\geq 1$, we define semibricks and wide subcategories in the $d$-extended hearts of bounded $t$-structures on a triangulated category. We show that these semibricks are in bijection with finite-length wide subcategories. When the $d$-extended heart is the $d$-extended module category $d\mbox{-}\mathrm{mod}Λ$ of a finite-dimensional algebra $Λ$ over a field, we define left/right-finite semibricks and left/right-finite wide subcategories in $d\mbox{-}\mathrm{mod}Λ$ and show bijections with $(d+1)$-term simple-minded collections, generalising the bijections between $2$-term simple-minded collections, left/right-finite wide subcategories and left/right-finite semibricks in $\mathrm{mod}Λ$. We use a relation between semibricks and silting complexes to characterise which mutations of $(d+1)$-term silting complexes are again $(d+1)$-term. |
| title | Semibricks and wide subcategories in extended module categories |
| topic | Representation Theory Rings and Algebras 16G10, 16E35, 18G80 |
| url | https://arxiv.org/abs/2511.08157 |