Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cartan subalgebras of root-reductive Lie algebras   Root-reductive Lie algebras are direct limits of finite-dimensional reductive
Lie algebras under injections which preserve the root spaces. It is known that
a root-reductive Lie algebra is a split extension of an abelian Lie algebra by
a direct sum of copies of finite-dimensional simple Lie algebras as well as
copies of the three simple infinite-dimensional root-reductive Lie algebras
sl_infty, so_infty, and sp_infty. As part of a structure theory program for
root-reductive Lie algebras, Cartan subalgebras of the Lie algebra gl_infty
were introduced and studied in a paper of Neeb and Penkov.
  In the present paper we refine and extend the results of [N-P] to the case of
a general root-reductive Lie algebra g. We prove that the Cartan subalgebras of
g are the centralizers of maximal toral subalgebras and that they are nilpotent
and self-normalizing. We also give an explicit description of all Cartan
subalgebras of the simple Lie algebras sl_infty, so_infty, and sp_infty.
  We conclude the paper with a characterization of the set of conjugacy classes
of Cartan subalgebras of the Lie algebras gl_infty, sl_infty, so_infty, and
sp_infty with respect to the group of automorphisms of the natural
representation which preserve the Lie algebra.

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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg