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| Author(s): |
Yuri Popov
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2020-09-30 |
| Examining board members: |
Artem Lopatin;
Ivan Chestakov;
Henrique Guzzo Junior;
Plamen Emilov Kochloukov;
Victor Mikhaylovich Petrogradsky
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| Advisor: | Artem Lopatin |
| Abstract | |
Noncommutative Jordan algebras were introduced by Albert. He noted that the structure theories of alternative and Jordan algebras share so many nice properties that it is natural to conjecture that these algebras are members of a more general class with a similar theory. So he introduced the variety of noncommutative Jordan algebras defined by the Jordan identity and the flexibility identity. The class of noncommutative Jordan (super)algebras turned out to be vast: for example, apart from alternative and Jordan (super)algebras it contains quasiassociative (super)algebras, quadratic flexible (super)algebras and (super)anticommutative (super)algebras. However, the structure theory of this class is far from being nice. Nevertheless, a certain progress was made in the study of structure theory of noncommutative Jordan algebras (and, more generally, superalgebras). Particularly, simple algebras of this class were studied by many authors. Simple finite-dimensional central noncommutative Jordan superalgebras were described by Pozhidaev and Shestakov. Representations of alternative and Jordan superalgebras is a popular topic nowadays which was studied by many authors. In this work we study representations of noncommutative Jordan algebras. In particular, we classify the irreducible finite-dimensional representations of simple finite-dimensional noncommutative Jordan superalgebras over an algebraically closed field of characteristic 0 and prove Kronecker factorization theorems for some superalgebras (AU) | |
| FAPESP's process: | 16/16445-0 - Representations of (super)algebras of Jordan type |
| Grantee: | Yury Popov |
| Support Opportunities: | Scholarships in Brazil - Doctorate |