Semibrick-cosilting correspondence

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-05-02 DOI:10.1112/blms.70076

Ramin Ebrahimi, Alireza Nasr-Isfahani

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Abstract

Let $Λ$ be a finite-dimensional algebra. In this paper, we show that there is a natural bijection between cosilting modules in $Mod Λ$ and semibricks in $Mod Λ$ satisfying some condition. Also this bijection restricts to a bijection between all semibricks in $\mod Λ$ and a certain subclass of cosilting modules. These bijections are generalizations of Asai's correspondence (Int. Math. Res. Not. 16 (2020) 4993–5054) between support $τ^{-}$ -tilting modules and right finite semibricks.

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Semibrick-cosilting对应

设Λ $\Lambda$是一个有限维代数。在本文中，我们证明了在Mod Λ $\operatorname{Mod}\Lambda$中有一个自然的双射模块与在Mod Λ $\operatorname{Mod}\Lambda$中有一个满足一定条件的半砖块之间的双射。此外，这个双射限制了mod Λ $\operatorname{mod}\Lambda$中所有半块和某个编译模块子类之间的双射。这些对偶是Asai对偶的概括。数学。Res. Not. 16(2020) 4993-5054)之间的支持τ−$\tau ^-$ -倾斜模块和右有限半砖。

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