Automorphisms of semisimple real Lie algebras. (English. Russian original) Zbl 0707.17011

Khatskevich, Yu. G.

Funct. Anal. Appl. 23, No. 2, 156-157 (1989); translation from Funkts. Anal. Prilozh. 23, No. 2, 84-85 (1989).

Consider a simple complex Lie algebra \({\mathfrak g}^ c\) with real form \({\mathfrak g}\). Let \(Aut_ e{\mathfrak g}^ c\) be the group of all automorphisms of \({\mathfrak g}^ c\) generated by the elements of the form exp ad x with nilpotent ad x. Let \(Aut_ 0{\mathfrak g}\) be the inverse image of \(Aut_ e{\mathfrak g}^ c\) with respect to the map Aut \({\mathfrak g}\to Aut {\mathfrak g}^ c\), \(g\mapsto g\otimes 1\), and \(Aut_ 0({\mathfrak g},{\mathfrak h})\) be the subgroup of \(Aut_ 0{\mathfrak g}\) preserving the Cartan subalgebra \({\mathfrak h}\subset {\mathfrak g}\). The author deduces a necessary and sufficient condition for certain pairs of \(Aut_ 0({\mathfrak g},{\mathfrak h})\) to be conjugate.

Reviewer: I.Kolář

MSC:

17B40	Automorphisms, derivations, other operators for Lie algebras and super algebras
17B20	Simple, semisimple, reductive (super)algebras

Keywords:

quasi-inner automorphisms; conjugacy classes

References:

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