论文标题
球形扭曲函子的应用在与前置代数的根类别相关的代数中。
Applications of spherical twist functors to Lie algebras associated to root categories of preprojective algebras
论文作者
论文摘要
令$λ_Q$为有限的无量子Quiver $ Q $的非二氧化碳类型的前代数和$ d^b（\ Mathrm {Rep}^nλ_q）$是有限的dimension dimential dimential dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional dimensional类别。我们在根类别上定义球形扭曲函数$ \ mathcal {r} _ {λ_q} $ of $ d^b（\ MATHRM {rep}^nλ_q）$ $ \ mathcal {r} _ {r} _ {λ_q}）$ \ \ \ m athcal {r} _ {r} _ {λ_q} $由球形扭曲函数引起的$ \ mathcal {r} _ {λ_q} $。我们还提出了$ \ Mathfrak {g}（\ Mathcal {r} _ {λ_Q}）$的某些谎言subalgebras之间的猜想关系，$ \ Mathfrak {g}（\ Mathcal {r} _q）_与根类别$ \ MATHCAL {r} _Q $ $ q $相关的代数。
Let $Λ_Q$ be the preprojective algebra of a finite acyclic quiver $Q$ of non-Dynkin type and $D^b(\mathrm{rep}^n Λ_Q)$ be the bounded derived category of finite dimensional nilpotent $Λ_Q$-modules. We define spherical twist functors over the root category $\mathcal{R}_{Λ_Q}$ of $D^b(\mathrm{rep}^n Λ_Q)$ and then realize the Weyl group associated to $Q$ as certain subquotient of the automorphism group of the Ringel-Hall Lie algebra $\mathfrak{g}(\mathcal{R}_{Λ_Q})$ of $\mathcal{R}_{Λ_Q}$ induced by spherical twist functors. We also present a conjectural relation between certain Lie subalgebras of $\mathfrak{g}(\mathcal{R}_{Λ_Q})$ and $\mathfrak{g}(\mathcal{R}_Q)$, where $\mathfrak{g}(\mathcal{R}_Q)$ is the Ringe-Hall Lie algebra associated to the root category $\mathcal{R}_Q$ of $Q$.
