Abstract
The principal objective of this paper is the study of one of the types of linear groups defined in I [15]: the groups of automorphisms of central simple exceptional Jordan algebras. This can also be considered as the second step in a program of studying âexceptionalâ linear groups analogous to the exceptional simple Lie groups via non-associative algebras. The first step in this program has been taken in another paper ([13]) in which we studied the counterparts of the Lie groups of type G 2 as groups of automorphisms of Cayley algebras. In an analogous fashion the present paper deals with the counterparts of the Lie group F 4 as groups of automorphisms of exceptional Jordan algebras.
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