Octonions and cross product

• Grant number: 21/05051-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2021
• End date: July 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Eduardo Toffolo
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/21391-1 - Gauge theory and algebraic geometry, AP.TEM

Abstract

This project aims to study the construction of quaternions and octonions and their relationship with the binary cross product in three and seven dimensions. The materials used as reference will be the articles "The octonions", by John C. Baez, "Notes on the octonions", by Dietmar A. Salamon and Thomas Walpuski, "Stetige Lösungen linearer Gleichungssysteme", by Beno Eckmann, and "Vector cross products on manifolds", by Alfred Gray. (AU)