2018/12/21 by Niels G Gresnigt
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Basis (linear algebra) #Braid group #Braid theory #Clifford algebra #Construct (python library) #Fermion #Geometric and Algebraic Topology #Ribbon #Simple (philosophy) #hep-th #physics.gen-ph
paper · pdf · doi:10.1088/1742-6596/1194/1/012040
Proceeding paper for the 32nd International Colloquium on Group Theoretical Methods in Physics (Group32) held at Czech Technical University in Prague, Czech Republic in July 2018. 10 pages, 2 figures
arxiv created 2018/12/21 · openalex created_date 2019/01/11 · openalex publication_date 2019/04/01 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/06
Some curious structural similarities between a recent braid - and Hurwitz algebraic description of the unbroken internal symmetries for a single generations of Standard Model fermions were recently identified. The non-trivial braid groups that can be represented using the four normed division algebras are B 2 and , exactly those required to represent a single generation of fermions in terms of simple three strand ribbon braids. These braided fermion states can be identified with the basis states of the minimal left ideals of the Clifford algebra Cℓ (6), generated from the nested left actions of the complex octonions on itself. That is, the ribbon spectrum can be related to octonion algebras. Some speculative ideas relating to ongoing research that attempts to construct a unified theory based on braid groups and Hurwitz algebras are discussed.