One of the exceptional Lie groups.
Under the further subgroup inclusion this decomposes further as
as the generalized tangent bundle-structure to the 7-dimensional fiber space which one obtains as discussed at M-theory supersymmetry algebra – As an 11-dimensional boundary condition. Here is the ordinary tangent space itself, is interpreted as the local incarnation of the possible M2-brane charges, the M5-brane charges and as the charges of Kaluza-Klein monopoles.
|supergravity gauge group (split real form)||T-duality group (via toroidal KK-compactification)||U-duality||maximal gauged supergravity|
|1||S-duality||10d type IIB supergravity|
|SL O(1,1)||9d supergravity|
|SU(3) SU(2)||SL||8d supergravity|
|E9||2d supergravity||E8-equivariant elliptic cohomology|
Sergio L. Cacciatori, Francesco Dalla Piazza, Antonio Scotti, E7 groups from octonionic magic square (arXiv:1007.4758)
and more generally in
The proposal to make this hidden -symmetry manifest via exceptional generalized geometry is due to
Further discussion includes