Sufficient conditions for isomorphism between isotopes of nonassociative algebras

• Grant number: 22/14579-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2023
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Henrique Guzzo Junior
• Grantee: Daniel Eiti Nishida Kawai
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This research project consists of three lines of investigation about possible existence of isomorphism between isotopic nonassociative algebras.The first one is to describe isotopes of certain classes of algebras satisfying some identities. Namely, we shall consider generalized right alternative algebras, generalized standard algebras and $(\gamma,\delta)$-algebras. Some of these classes include alternative algebras as particular examples. Moreover, all these algebras are power-associative.The second part consists in to study the characterization of normed algebras without joint zero divisors which are either generalized right alternative algebras, generalized standard algebras or $(\gamma,\delta)$-algebras.And the last goal is an attempt to obtain the classification of absolute valued algebras of algebraic degree at most $4$. It is known that every algebraic absolute valued algebra has algebraic degree $1$, $2$, $4$ or $8$. Moreover, this problem was solved for the case of the algebraic degree at most $2$.