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| Author(s): |
Pedro Souza Fagundes
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: | 2024-01-24 |
| Examining board members: |
Plamen Emilov Kochloukov;
Carla Rizzo;
Antonio Ioppolo;
Diogo Diniz Pereira da Silva e Silva;
Viviane Ribeiro Tomaz da Silva
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| Advisor: | Matej Bresar; Plamen Emilov Kochloukov |
| Abstract | |
The main goal of this thesis is to present results in the direction of three distinct problems. We show that graded algebras which are sum of two homogeneous subalgebras satisfying graded identities are not always gr-PI algebras. Moreover, we give sufficient conditions for the sum to satisfy some graded polynomial identity. We consider images of multilinear graded polynomials on the graded algebra of upper triangular matrices and we classify such images for certain gradings. We obtain a full description in the case of small dimension for the ordinary and Jordan settings. We also study the case of upper triangular matrices with graded involution and of small dimension, where we classify the images of multilinear polynomials on these algebras, moreover we show that such images are not always vector subspaces. A generalization of zpd algebras is presented (the so called f-zpd algebras) and we prove that the full matrix algebra is not always f-zpd. We give several examples of polynomials f where the full matrix algebra is f-zpd, and we also consider a problem of Nullstellensatz type which is related to the class of algebras introduced (AU) | |
| FAPESP's process: | 19/16994-1 - Algebras that are sums of two PI subalgebras |
| Grantee: | Pedro Souza Fagundes |
| Support Opportunities: | Scholarships in Brazil - Doctorate |