Sextonions,Zorn matrices,and $$\mathbf {e}_{\mathbf{7} \frac{\mathbf{1}}{\mathbf{2}}}$$ |
| |
| Authors: | Alessio Marrani Piero Truini |
| |
| Institution: | 1.Centro Studi e Ricerche “Enrico Fermi”,Rome,Italy;2.Dipartimento di Fisica e Astronomia “Galileo Galilei”,Università di Padova and INFN, Sezione di Padova,Padua,Italy;3.Dipartimento di Fisica,Università degli Studi and INFN, Sezione di Genova,Genoa,Italy |
| |
| Abstract: | By exploiting suitably constrained Zorn matrices, we present a new construction of the algebra of sextonions (over the algebraically closed field \(\mathbb {C}\)). This allows for an explicit construction, in terms of Jordan pairs, of the non-semisimple Lie algebra \(\mathbf {e}_{\mathbf{7} \frac{\mathbf{1}}{\mathbf{2}}}\), intermediate between \(\mathbf {e_7}\) and \(\mathbf {e_8}\), as well as of all Lie algebras occurring in the sextonionic row and column of the extended Freudenthal Magic Square. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
