Ore Domainas: localizations, invariants and representations.

• Grant number: 18/18146-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2018
• End date: November 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Vyacheslav Futorny
• Grantee: João Fernando Schwarz
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this post-doctoral project, we plan to study invariants of many Ore domains which have infinite dimension over their center. In particular: rings of differential operators, certain quantum groups, and the important class of Galois algebras. We have interest in structural aspects, in special the localization of these rings of invariantes, and also interest in representation theoretical aspects, in particular Gelfand-Tsetlin categories.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FUTORNY, VYACHESLAV; SCHWARZ, JOAO. Algebras of invariant differential operators. Journal of Algebra, v. 542, p. 215-229, JAN 15 2020. (18/18146-5, 16/14648-0, 14/25612-1, 18/23690-6)

FUTORNY, VYACHESLAV; SCHWARZ, JOAO; SHESTAKOV, IVAN. LD-stability for Goldie rings. Journal of Pure and Applied Algebra, v. 225, n. 11, NOV 2021. (18/23690-6, 18/18146-5)

SCHWARZ, JOAO. Poisson No ether's Problem and Poisson rationality. Journal of Algebra, v. 606, p. 14-pg., 2022-05-20. (18/18146-5)

FUTORNY, VYACHESLAV; SCHWARZ, JOAO. Holonomic modules for rings of invariant differential operators. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v. 31, n. 04, p. 605-622, JUN 2021. (18/18146-5, 18/23690-6)