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- W4300868139 abstract "A subcategory of an abelian category is wide if it is closed under sums, summands, kernels, cokernels, and extensions. Wide subcategories provide a significant interface between representation theory and combinatorics. If $Phi$ is a finite dimensional algebra, then each functorially finite wide subcategory of $operatorname{mod}( Phi )$ is of the form $phi_{ * }big( operatorname{mod}( Gamma ) big)$ in an essentially unique way, where $Gamma$ is a finite dimensional algebra and $Phi stackrel{ phi }{ longrightarrow } Gamma$ is an algebra epimorphism satisfying $operatorname{Tor}^{ Phi }_1( Gamma,Gamma ) = 0$. Let ${mathcal F} subseteq operatorname{mod}( Phi )$ be a $d$-cluster tilting subcategory as defined by Iyama. Then ${mathcal F}$ is a $d$-abelian category as defined by Jasso, and we call a subcategory of ${mathcal F}$ wide if it is closed under sums, summands, $d$-kernels, $d$-cokernels, and $d$-extensions. We generalise the above description of wide subcategories to this setting: Each functorially finite wide subcategory of ${mathcal F}$ is of the form $phi_{ * }( {mathcal G} )$ in an essentially unique way, where $Phi stackrel{ phi }{ longrightarrow } Gamma$ is an algebra epimorphism satisfying $operatorname{Tor}^{ Phi }_d( Gamma,Gamma ) = 0$, and ${mathcal G} subseteq operatorname{mod}( Gamma )$ is a $d$-cluster tilting subcategory. We illustrate the theory by computing the wide subcategories of some $d$-cluster tilting subcategories ${mathcal F} subseteq operatorname{mod}( Phi )$ over algebras of the form $Phi = kA_m / (operatorname{rad},kA_m )^{ ell }$." @default.
- W4300868139 created "2022-10-04" @default.
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- W4300868139 date "2017-05-05" @default.
- W4300868139 modified "2023-09-30" @default.
- W4300868139 title "Wide subcategories of $d$-cluster tilting subcategories" @default.
- W4300868139 doi "https://doi.org/10.48550/arxiv.1705.02246" @default.
- W4300868139 hasPublicationYear "2017" @default.
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