# the intersection of all borel subalgebra for a complex semisimple Lie algebra

maybe my question is trivial ,but I can not find any reference or paper about the question. my question is as follows, Let $g$ be a finite dimensinal complex semisimple Lie algebra,what is the intersection of all borel subalgebra?or what is the intersection all cartan subalgebra?

in general,two general cartan subalgebras are conjugate. and my question is, what is the intersection of them?

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Hint: conjugacy implies intersection is a Lie ideal. Try to figure our the rest for yourself. –  Boyarsky Jun 21 '10 at 3:40
thank you very much –  chiong Jun 21 '10 at 3:48
As Boyarsky says, this is basically an exercise in the use of some standard structure theory of complex Lie algebras. How to approach it depends on what you already know, but it's instructive to remove the word "semisimple" and deal more generally with the old concept of (solvable) "radical". The notion of "Borel subalgebra" actually came in somewhat late in the historical development, while "Cartan subalgebras" in some form have always been there. Anyway, the answer to the question is elementary. –  Jim Humphreys Jun 21 '10 at 12:07