# Division algebraic symmetry breaking

### APA

Furey, C. (2021). Division algebraic symmetry breaking . Perimeter Institute. https://pirsa.org/21020027

### MLA

Furey, Cohl. Division algebraic symmetry breaking . Perimeter Institute, Feb. 22, 2021, https://pirsa.org/21020027

### BibTex

@misc{ pirsa_PIRSA:21020027, doi = {10.48660/21020027}, url = {https://pirsa.org/21020027}, author = {Furey, Cohl}, keywords = {Mathematical physics}, language = {en}, title = {Division algebraic symmetry breaking }, publisher = {Perimeter Institute}, year = {2021}, month = {feb}, note = {PIRSA:21020027 see, \url{https://pirsa.org}} }

Humboldt University of Berlin

Talk Type

**Subject**

Abstract

Can the 32C-dimensional algebra RCHO offer anything new for particle physics? Indeed it can. Here we identify a sequence of complex structures within RCHO 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. It should be noted that this pattern would not have been obvious within the standard formalism.