Full text
| |
| Author(s): |
Felipe Yukihide Yasumura
Total Authors: 1
|
| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2018-12-06 |
| Examining board members: |
Plamen Emilov Kochloukov;
Onofrio Mario Di Vincenzo;
Eli Aljadeff;
Daniela La Mattina;
Ivan Chestakov
|
| Advisor: | Plamen Emilov Kochloukov; Yuri Bahturin |
| Abstract | |
In this thesis, we classify group gradings on the algebra of upper triangular matrices, viewed as Lie and Jordan algebras, over an arbitrary field and arbitrary grading group. Using this result, and assuming stronger conditions, we were able to obtain the classification of group gradings on the algebra of block-triangular matrices, viewed as Lie and Jordan algebras. We compute the asymptotic behavior of the graded codimension sequence for any grading on the associative algebra of upper-triangular matrices. For the Lie case, we obtain a partial result for the asymptotic behavior of graded codimensions, and we compute the graded exponent of all gradings on the upper triangular matrices, as Lie and Jordan algebras. Finally, we investigate the problem of determining a simple algebra by its polynomial identities. We prove that finite-dimensional graded $\Omega$-algebras, which are graded-prime, over an algebraically closed field are uniquely determined by their graded polynomial identities (AU) | |
| FAPESP's process: | 13/22802-1 - Graded identities in Lie and Jordan algebras |
| Grantee: | Felipe Yukihide Yasumura |
| Support Opportunities: | Scholarships in Brazil - Doctorate |