Abstract
The N-extended D=7 De Sitter algebras U α U(4, N; H) with bosonic sector SO(6,2) × Sp( N), describing also N-extended D=6 superconformal symmetries are given. The quaternionic structure of real representation is described by three real quaternionic Majorana conditions. We conjecture that N=2 D=7 De Sitter supergroup U αU(4,2;H) describes the supersymmetries of the vacuum solution for D=11 supergravity, with the space-time described by seven-dimensional De Sitter space and internal space S 4.
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