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Periodic Automorphisms of Semisimple Lie algebras
Classical invariant theory of Chevalley and Kostant relates geometric properties of the adjoint representation of a semisimple group G to algebraic properties of its Lie algebra. A well-known generalization of this set-up is the symmetric space decomposition, which arises naturally when one considers an involutive automorphism of G. But in fact, Vinberg showed that much of this theory extends to the case of an arbitrary automorphism of finite order. Here we will show how Vinberg's work can be established in characteristic zero, and how this work has shed light on a long-standing conjecture of Popov in the field.
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