Graded identities in Lie and Jordan algebras

• Grant number: 13/22802-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2014
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Plamen Emilov Kochloukov
• Grantee: Felipe Yukihide Yasumura
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 10/50347-9 - Algebras, representations e applications, AP.TEM
• Associated scholarship(s): 17/11018-9 - Graded identities on finite dimensional graded simple Lie álgebras, BE.EP.DR

Abstract

We shall study graded identities in Lie and Jordan algebras. We shall work with the gradings and the graded identities for the Lie algebra of the upper triangular matrices of size nxn over a field K. We shall be studying also the graded identities for the Jordan algebra of the upper triangular matrices. In both cases we aim at considering all possible gradings by finite groups. Having concluded this step we shall be passing on to graded identities in other classes of algebras.The student is now at his last semester of the master program in mathematics. He has already done in practice all courses that are relevant for the PhD program in Mathematics. He has already obtained all credits necessary for the PhD program. We expect that he will be able to sit the first qualification exam in July 2014 (if not in December 2013, before even commencing his PhD studies). Felipes master thesis defence is scheduled for the end of February 2014. We want to stress that the student has achieved top marks during his master studies (most A, and moreover numerical notes in various of the courses 10.0).

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

KOSHLUKOV, PLAMEN; YUKIHIDE, FELIPE. Elementary gradings on the Lie algebra UTn(-). Journal of Algebra, v. 473, p. 66-79, MAR 1 2017. (13/22802-1, 14/09310-5)

KOSHLUKOV, PLAMEN; YUKIHIDE, FELIPE. Group gradings on the Lie algebra of upper triangular matrices. Journal of Algebra, v. 477, p. 294-311, MAY 1 2017. (14/09310-5, 13/22802-1)

HITOMI, EDUARDO; KOSHLUKOV, PLAMEN; YASUMURA, FELIPE. Group gradings on the Lie and Jordan algebras of upper triangular matrices. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 11, n. 2, p. 326-347, DEC 2017. (14/09310-5, 13/22802-1)

YASUMURA, FELIPE YUKIHIDE; KOSHLUKOV, PLAMEN EMILOV. Asymptotics of graded codimension of upper triangular matrices. Israel Journal of Mathematics, v. 223, n. 1, p. 423-439, FEB 2018. (14/09310-5, 13/22802-1)

KOSHLUKOV, PLAMEN; YASUMURA, FELIPE YUKIHIDE. Group gradings on the Jordan algebra of upper triangular matrices. Linear Algebra and its Applications, v. 534, p. 1-12, DEC 1 2017. (13/22802-1, 14/09310-5)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

YASUMURA, Felipe Yukihide. Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais. 2018. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.