Título:
Strong equivalence of graded algebras
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Autor:
Abadie, Fernando
Dokuchaev, Michael
Exel, Ruy
Dokuchaev, Michael
Exel, Ruy
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Tipo de documento:
Preprint
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MORITA EQUIVALENCE
RADED ALGEBRA
PARTIAL ACTION
SKEW GROUP RING
SMASH PRODUCT
RADED ALGEBRA
PARTIAL ACTION
SKEW GROUP RING
SMASH PRODUCT
Año de publicación:
2024
Contenido:
Resumen:
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 algebra
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Versión permitida preprint.
Publicado también en: Journal of Algebra, 2024, 659(1): 818-858. DOI: 10.1016/j.jalgebra.2024.07.014
Publicado también en: Journal of Algebra, 2024, 659(1): 818-858. DOI: 10.1016/j.jalgebra.2024.07.014
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arXiv
EN:
Mathematics (Rings and Algebras). arXiv:2201.03513, jul. 2024, pp.1-38
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Citación:
Abadie, F, Dokuchaev, M y Exel, R. "Strong equivalence of graded algebras". [Preprint]. Publicado en: Mathematics (Rings and Algebras). 2024, arXiv.2201.03513, jul. 2024, pp.1-38. DOI: 10.48550/arXiv.2201.03513
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2201.03513v2.pdf | — | 418.37 KB | Adobe PDF |