TL;DR: In this paper, the SO(8) supergravity theory was derived by dimensional reduction of the super gravity theory in 11 dimensions to 4 dimensions, where the equations of motion are invariant under the global non-compact group E7(+7).
TL;DR: In this article, the q-version of the Weyl group for quantized universal enveloping algebras of simple Lie groups is defined and explicit multiplicative formulas for the universal R-matrix are given.
Abstract: We define theq-version of the Weyl group for quantized universal enveloping algebras of simple Lie group and we find explicit multiplicative formulas for the universalR-matrix.