Super polynomial identities of simple superalgebras

• Grant number: 23/03922-8
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2023
• End date: June 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Felipe Yukihide Yasumura
• Grantee: Felipe Yukihide Yasumura
• Host Investigator: Yuri Bahturin
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Memorial University of Newfoundland (MUN), Canada
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM

Abstract

We shall investigate if a simple nonassociative superalgebra is uniquely determined by its superpolynomial identities. The ordinary version of this question attracted the attention of several people until Razmyslov's result, where a celebrated version of the problem is solved in the context of Omega-algebras. Then, extending the question to the context of graded algebras or algebras with an additional structure is natural. The solution of the graded version of the problem is done by the candidate jointly with the proposed supervisor. A natural counterpart, which is historically significant and the main objective of the present research proposal, is to investigate the superpolynomial identities of a given algebra. (AU)