Quaternionic and octonionic spinors. A classification

Quaternionic and octonionic realizations of Clifford algebras and spinors areclassified and explicitly constructed in terms of recursive formulas. The mostgeneral free dynamics in arbitrary signature space-times for both quaternionicand octonionic spinors is presented. In the octonionic case we further providea systematic list of results and tables expressing, e.g., the relations of theoctonionic Clifford algebras with the $G_2$ cosets over the Lorentz algebras,the identities satisfied by the higher-rank antisymmetric octonionic tensorsand so on. Applications of these results range from the classification ofoctonionic generalized supersymmetries, the construction of octonionicsuperstrings, as well as the investigations concerning the recently discoveredoctonionic $M$-superalgebra and its superconformal extension.Comment: 24 pages, LaTe