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edit approved Dec 21, 2014 at 15:45
Aaron Maroja
edit approved Dec 21, 2014 at 15:45
Aaron Maroja
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Suppose that g$g$ is a complex semisimplesemi-simple Lie algebra and g'$g'$ its reductive subalgebra. 

If \tau$\tau$ is an involutive automorphism of g'$g'$, can \tau$\tau$ be extended to an involutive automorphism of g$g$ in general?

If not in general, for what kind of pair (g, g')$(g, g')$ or \tau$\tau$, this is true?

Suppose that g is a complex semisimple Lie algebra and g' its reductive subalgebra. If \tau is an involutive automorphism of g', can \tau be extended to an involutive automorphism of g in general?

If not in general, for what kind of pair (g, g') or \tau, this is true?

Suppose that $g$ is a complex semi-simple Lie algebra and $g'$ its reductive subalgebra. 

If $\tau$ is an involutive automorphism of $g'$, can $\tau$ be extended to an involutive automorphism of $g$ in general?

If not in general, for what kind of pair $(g, g')$ or $\tau$, this is true?

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Hebe
Hebe
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Extension of an involutive automorphism

Suppose that g is a complex semisimple Lie algebra and g' its reductive subalgebra. If \tau is an involutive automorphism of g', can \tau be extended to an involutive automorphism of g in general?

If not in general, for what kind of pair (g, g') or \tau, this is true?