论文标题
分级代数的强度
Strong equivalence of graded algebras
论文作者
论文摘要
我们介绍了分级代数之间有很强的等效性的概念，并证明了一个组$ g $的任何部分分级的代数都与偏差集团代数相同，这是$ g $的偏差组代数。至于更一般的diDempotent分级代数$ b $，我们指出，科恩 - 蒙特哥马利二元性符合$ b $，而$ b $的分级与全球偏斜集团代数等同。我们表明，强度的等效性可保留强大的等级，并且与产品部分作用的莫里塔等效性很好。此外，我们证明，任何产品部分群体行动$α$都是全球化的，可以全球化；如果这样的全球化$β$很少，则偏斜组代数为$α$，$β$是等效的；此外，$β$是莫里塔等价的独特之处。最后，我们表明，作为分级代数，强烈分级等效的部分阶层的代数稳定同构。
We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group $G$ is strongly-graded-equivalent to the skew group algebra by a product partial action of $G$. As to a more general idempotent graded algebra $B$, we point out that the Cohen-Montgomery duality holds for $B$, and $B$ is graded-equivalent to a global skew group algebra. We show that strongly-graded-equivalence preserves strong gradings and is nicely related to Morita equivalence of product partial actions. Furthermore, we prove that any product partial group action $α$ is globalizable up to Morita equivalence; if such a globalization $β$ is minimal, then the skew group algebras by $α$ and $β$ are graded-equivalent; moreover, $β$ is unique up to Morita equivalence. Finally, we show that strongly-graded-equivalent partially-strongly-graded algebras are stably isomorphic as graded algebras.
