Granded identities in non associative algebras

Author(s)

Diogo Diniz Pereira da Silva e Silva

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP)
• Defense date: 2010-12-13

Examining board members

Plamen Emilov Kochloukov; Antonio José Engler; Ivan Chestakov; Iyana Kashuba; Victor Petrograndskiy

• Advisor: Plamen Emilov Kochloukov

Abstract

In this thesis we study graded identities in non associative algebras. Namely we study graded polynomial identities for the Lie algebra of the 2_2 matrices with trace zero with it's three natural gradings, the Z2-grading, the Z2_Z2-grading and the Z-grading, in this case we obtained a new proof of the results of [27] that doesn't involve use of Invariant Theory, this results were published in [30]. We also studied the graded identities of the Jordan algebra of the symmetric matrices of order two, we obtained basis for the graded identities of this Jordan algebra in all possible gradings, we also obtained basis for the weak identities of the pairs (Bn; Jn) and (B; J), where Bn and B are the Jordan algebras of a symmetric bilinear form in a the vector spaces Vn and V respectively, where Vn has dimension n and V has countable dimension, this results are in the article [29], accepted for publication (AU)

• FAPESP's process: 07/00447-4 - Graded identities in Lie Algebras
• Grantee: Diogo Diniz Pereira da Silva e Silva
• Support Opportunities: Scholarships in Brazil - Doctorate