Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradings on Lie algebras with applications to infra-nilmanifolds   In this paper, we study positive as well as non-negative and non-trivial
gradings on finite dimensional Lie algebras. We give a different proof that the
existence of such a grading on a Lie algebra is invariant under taking field
extensions, a result very recently obtained by Y. Cornulier. Similarly, we
prove that given a grading of one these types and a finite group of
automorphisms, there always exist a positive grading which is preserved by this
group. From these results we conclude that the existence of an expanding map or
a non-trivial self-cover on an infra-nilmanifold depends only on the covering
Lie group. Another application is the construction of a nilmanifold admitting
an Anosov diffeomorphism but no non-trivial self-covers and in particular no
expanding maps, which is the first known example of this type.

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The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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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: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: eess