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- W4300471922 abstract "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." @default.
- W4300471922 created "2022-10-03" @default.
- W4300471922 creator A5017555794 @default.
- W4300471922 date "2014-10-14" @default.
- W4300471922 modified "2023-09-29" @default.
- W4300471922 title "Gradings on Lie algebras with applications to infra-nilmanifolds" @default.
- W4300471922 doi "https://doi.org/10.48550/arxiv.1410.3713" @default.
- W4300471922 hasPublicationYear "2014" @default.
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