Space-time symmetries of superstring and Jordan algebras
The authors consider the Jordan algebras \({\mathfrak M}^ 1_ 3\), \({\mathfrak M}^ 2_ 3\), \({\mathfrak M}^ 4_ 3\), and \({\mathfrak M}^ 8_ 3\) whose elements are the \(3\times 3\) Hermitian matrices with, respectively, real, complex, quaternionic, and octonionic elements. The covering groups of the Lorentz groups for, respectively, dimensions 3, 4, 6, and 10 can be expressed as subgroups of the reduced structure groups of these algebras, which are suitable generalizations of the automorphism groups. The authors point out a connection between the structure groups or the automorphism groups of the mentioned Jordan algebras and the symmetries of superstrings.
scientific article; zbMATH DE number 4168911