Abstract
In this paper the geometric interpretation of the exceptional Lie groups F4, E6, E7, and E8 is given. These groups are groups of motions of elliptic hyperbolic planes over nonassociative algebras of octaves and split octaves and their tensor products with algebras of usual and split complex numbers, quaternions and octaves. The explicit expressions of motions of these planes and their figures of symmetry are presented.
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