Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the case where Adjoint and Coadjoint Orbit Spaces are
  Symplectomorphic   Let G be an n-dimensional semisimple compact and connected Lie group acting
on both the Lie algebra g of G and its dual g*. We show that a nondegenerate
Killing form of G induces an Ad*-equivariant isomorphism of g onto g* which, in
turn, induces by passage to quotients a symplectomorphism between adjoint and
coadjoint orbit spaces of G.

25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph