Partial actions, Galois cohomology and seven term exact sequences

• Grant number: 23/14066-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 02, 2024
• End date: January 01, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Mikhailo Dokuchaev
• Visiting researcher: Hector Edonis Pinedo Tapia
• Visiting researcher institution: Universidad Industrial De Santander/Uis, Colombia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 20/16594-0 - Non commutative rings and applications, AP.TEM

Abstract

Apply to partial Galois extensions of rings a seven term exact sequence recently obtained for non-commutative rings and a partial representation, which in the case of a Galois extension of non-commutative rings would give a new sequence, and in the case of commutative rings would give an alternative proof for a sequence produced earlier. Study the exact sequences of Chase-Harrison-Rosenberg type obtained in the context of partial actions and partial representations from the point of view of globalization. Investigate the relation of the Chase-Rosenberg exact sequence involving Amitsur cohomology with the Chase-Harrison-Rosenberg type exact sequence obtained for partial Galois extensions of commutative rings. (AU)