Strong equivalence of graded algebras

Author(s)

Abadie, F. ; Dokuchaev, M. ; Exel, R.

• Document type: Journal article
• Source: Journal of Algebra; v. 659, p. 41-pg., 2024-07-30.

Abstract

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 alpha is globalizable up to Morita equivalence; if such a globalization /3 is minimal, then the skew group algebras by alpha and /3 are graded-equivalent; moreover, /3 is unique up to Morita equivalence. Finally, we show that strongly-graded-equivalent partially-strongly-graded algebras with orthogonal local units are stably isomorphic as graded algebras. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU)

• FAPESP's process: 20/16594-0 - Non commutative rings and applications
• Grantee: Francisco Cesar Polcino Milies
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 17/23242-0 - From graded algebras to crossed products
• Grantee: Mikhailo Dokuchaev
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 17/26645-9 - Thermodynamic formalism and KMS states on Countable Markov shifts
• Grantee: Rodrigo Bissacot Proença
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• FAPESP's process: 15/09162-9 - Non commutative algebra and applications
• Grantee: Francisco Cesar Polcino Milies
• Support Opportunities: Research Projects - Thematic Grants