Spaces With Exceptional Fundamental Groups
Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 97
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The geometric interpretations of all real exceptional simple
Lie groups of classes $G_2$, $F_4$, $E_6$, $E_7$ and $E_8$ are
described. In particular, we describe the interpretations of the four
last classes as groups of motions of elliptic and hyperbolic planes
over algebras of octaves and split octaves and over tensor products of
them and algebras of usual and split complex numbers, quaternions and
octaves. The explicite expressions of motions of these planes are
found. The symmetry figures and parabolic figures of all considered
spaces and geometric interpretations of all fundamental linear
representations of real exceptional simple Lie groups are found.
Classification :
51F99 53C35 22E46
@article{PIM_1993_N_S_54_68_a13,
author = {Boris A. Rosenfeld},
title = {Spaces {With} {Exceptional} {Fundamental} {Groups}},
journal = {Publications de l'Institut Math\'ematique},
pages = {97 },
publisher = {mathdoc},
volume = {_N_S_54},
number = {68},
year = {1993},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a13/}
}
Boris A. Rosenfeld. Spaces With Exceptional Fundamental Groups. Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 97 . http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a13/