##
**Video URL**
http://pirsa.org/21030013

## Abstract

Can the 32C-dimensional algebra R(x)C(x)H(x)O offer anything new for particle physics? Indeed it can. Here we identify a sequence of complex structures within R(x)C(x)H(x)O which sets in motion a cascade of breaking symmetries: Spin(10) -> Pati-Salam -> Left-Right symmetric -> Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers. Finally, we describe a left-right symmetric Higgs system which exhibits, we believe for the first time, an explicit demonstration of quaternionic triality.

## Details

**Talk Number**21030013

**Speaker Profile**

**Date**

**Source**

Perimeter Institute Recorded Seminar Archive

- Mathematical physics
- Particle Physics
- Quantum Fields and Strings

**Scientific Area**

- Conference

**Talk Type**