| Grant number: | 17/25777-9 |
| Support Opportunities: | Scholarships abroad - Research |
| Effective date (Start): | September 03, 2018 |
| Effective date (End): | July 02, 2019 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |
| Principal Investigator: | Iryna Kashuba |
| Grantee: | Iryna Kashuba |
| Host Investigator: | Vera Serganova |
| Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Research place: | University of California, Berkeley (UC Berkeley), United States |
| Associated research grant: | 14/09310-5 - Algebraic structures and their representations, AP.TEM |
Abstract The goal of this project is to explore relationship between representations of a Jordan (super)algebra J and a graded Lie (super)algebra g obtained from J by the Tits-Kantor-Koecher construction. The representation theory of Jordan and especially Lie superalgebras was used in theoretical physics to describe the mathematics of supersymmetry and since the became a prominent field with the notable impact on mathematics as a whole. The representation theory of Lie superalgebras has been known, since its inception, to be much more complicated than the corresponding theory for Lie algebras, nevertheless it is extensively studied. From the other side Jordan theory is much closer to Lie theory in supercase. In particular the famous bridge (the TKK construction) between Lie and Jordan theory proved to be the most useful for both superalgebras and superrepresentation. (AU) | |
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