Graded identities on finite dimensional graded simple Lie álgebras

• Grant number: 17/11018-9
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: August 01, 2017
• End date: July 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Plamen Emilov Kochloukov
• Grantee: Felipe Yukihide Yasumura
• Supervisor: Yuri Bahturin
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Memorial University of Newfoundland (MUN), Canada
• Associated to the scholarship: 13/22802-1 - Graded identities in Lie and Jordan algebras, BP.DR

Abstract

We shall study the graded identities for an elementary grading on the Lie algebra of upper triangular matrices. To this end we shall study the combinatorial properties of certain subset of the permutation group of m elements. Moreover we are planning to approach the following problem. Given two finite dimensional graded simple Lie algebras over an algebraically closed field, satisfying the same graded polynomial identities, are they isomorphic as graded algebras?