论文标题
支持$τ$ - 在小组分级代数上使用模块和半复杂
Support $τ$-tilting modules and semibricks over group graded algebras
论文作者
论文摘要
我们考虑一个有限的尺寸强烈的$ g $的代数$ a $，带有{自注} $ 1 $ -COMPONENT $ b $，在我们的主要结果中，我们证明，从$ b $到$ a $ a $ a $ b $ b $ b $ us-modules $τ$τ$τ$的$ the $ A $ A $ A $ A $ a g（a） $ m $是$ g $ invariant。类似的声明也适用于$ a $ a $ to $ b $的限制，因此我们的结果可能被视为Clifford和Maschke Type Theorems，以$ 2 $ - 期的Silting Complexs。我们还将应用于半纤维和相关的宽子类别。
We consider a finite dimensional strongly $G$-graded algebra $A$ with { self-injective} $1$-component $B$, and in our main result we prove that the induction from $B$ to $A$ of a basic support $τ$-tilting pair of $B$-modules is a support $τ$-tilting pair $(M,P)$ of $A$-modules if and only if $M$ is $G$-invariant. A similar statement holds for the restriction from $A$ to $B$, so our results may be viewed as Clifford and Maschke type theorems for $2$-term silting complexes. We also give applications to semibricks and the associated wide subcategories.
