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Do generalized Kac-Moody lie algebras of infinite dimension contain subalgebras of finite codimension? If so, is there a classification?

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    $\begingroup$ Can you clarify what you mean by "finite index"? Do you mean "finite codimension"? $\endgroup$
    – Jim Humphreys
    Commented Jan 2, 2015 at 18:46
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    $\begingroup$ Yes, finite codimension as a vector space. Is there another possible interpretation? $\endgroup$
    – Ian Agol
    Commented Jan 2, 2015 at 18:48
  • $\begingroup$ Thanks for the clarification. Usually "finite index" has meaning only in a group-theoretic context. $\endgroup$
    – Jim Humphreys
    Commented Jan 2, 2015 at 22:09
  • $\begingroup$ Right, I think this was just a typo on my part. $\endgroup$
    – Ian Agol
    Commented Jan 2, 2015 at 22:19
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    $\begingroup$ Beware (in contrast to the group setting) that the existence of a proper finite-codimensional subalgebra does not imply that of such an ideal. For instance Amayo (Quasi-ideals of Lie algebras II, Proc. London Math. Soc. (3) 33, 1976, 37-64) constructed an infinite-dimensional simple Lie algebra with a subalgebra of codimension 1. $\endgroup$
    – YCor
    Commented Jan 3, 2015 at 12:35

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