Exotic holonomies $\E_7^{(a)}$

Details Exotic holonomies $\E_7^{(a)}$ Exotic holonomies $\E_7^{(a)}$

1996-07-18

arxiv.org/abs/dg-ga/9607004v1

Internat. J. Math. 8 (1997) No.5, 583-594.

Mathematics

Differential Geometry

LaTeX, 10 pages

Scientific paper

It is proved that the Lie groups $\E_7^{(5)}$ and $\E^{(7)}_7$ represented in $\R^{56}$ and the Lie group $\E_7^{\C}$ represented in $\R^{112}$ occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connnections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of positive dimension.

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