The reductive pair \((B_4, B_3)\) and affine connections on \(S^{15}\)
The authors continue their investigations of reductive pairs of Lie algebras \((L,H)\). In particular they determine the attached connection algebras and related tensors for \((B_4, B_3)\). When restricted to the real field, it is shown that there is a three parameter family of Spin(9)-invariant affine connections on \(S^{15}\). They find five different possibilities for the holonomy algebra of a connection algebra attached to \((B_4, B_3)\).
scientific article; zbMATH DE number 1471030