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• W2963695411 abstract "This paper looks for Frobenius subcategories, via the separated monomorphism category $operatorname {smon}(Q, I, mathscr {X})$, and on the other hand, aims to establish an RSS equivalence from $operatorname {smon}(Q, I, mathscr {X})$ to its dual $operatorname {sepi}(Q, I, mathscr {X})$. For a bound quiver $(Q, I)$ and an algebra $A$, where $Q$ is acyclic and $I$ is generated by monomial relations, let $Lambda =Aotimes _k kQ/I$. For any additive subcategory $mathscr {X}$ of $A$-mod, we introduce $operatorname {smon}(Q, I, mathscr {X})$ combinatorially. It describes Gorenstein-projective $Lambda$-modules as $mathcal {GP}(Lambda ) = operatorname {smon}(Q, I, mathcal {GP}(A))$. It admits a homological interpretation and enjoys a reciprocity $operatorname {smon}(Q, I, ^bot T)= ^bot (Totimes kQ/I)$ for a cotilting $A$-module $T$. As an application, $operatorname {smon}(Q, I, mathscr {X})$ has Auslander-Reiten sequences if $mathscr {X}$ is resolving and contravariantly finite with $widehat {mathscr {X}}=$𝐴-mod . In particular, $operatorname {smon}(Q, I, A)$ has Auslander-Reiten sequences. It also admits a filtration interpretation as $operatorname {smon}(Q, I, mathscr {X})=operatorname {Fil}(mathscr {X}otimes mathcal P(kQ/I))$, provided that $mathscr {X}$ is extension-closed. As an application, $operatorname {smon}(Q, I, mathscr {X})$ is an extension-closed Frobenius subcategory if and only if so is $mathscr {X}$. This gives “new” Frobenius subcategories of $Lambda$-mod in the sense that they may not be $mathcal {GP}(Lambda )$. Ringel-Schmidmeier-Simson equivalence $operatorname {smon}(Q, I, mathscr {X})cong operatorname {sepi}(Q, I, mathscr {X})$ is introduced and the existence is proved for arbitrary extension-closed subcategories $mathscr {X}$. In particular, the Nakayama functor $mathcal N_Lambda$ gives an RSS equivalence $operatorname {smon}(Q, I, A)cong operatorname {sepi}(Q, I, A)$ if and only if $A$ is Frobenius. For a chain $Q$ with arbitrary $I$, an explicit formula of an RSS equivalence is found for arbitrary additive subcategories $mathscr {X}$." @default.
• W2963695411 created "2019-07-30" @default.
• W2963695411 creator A5021693466 @default.
• W2963695411 creator A5066805987 @default.
• W2963695411 date "2019-04-18" @default.
• W2963695411 modified "2023-10-14" @default.
• W2963695411 title "Separated monic representations II: Frobenius subcategories and RSS equivalences" @default.
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• W2963695411 doi "https://doi.org/10.1090/tran/7622" @default.
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