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Representations of Jordan superalgebras

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


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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Scientific publications
(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)
KASHUBA, IRYNA; SERGANOVA, VERA. Representations of simple Jordan superalgebras. ADVANCES IN MATHEMATICS, v. 370, . (17/25777-9)

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