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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.03513 |
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Table of Contents:
- 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.