Geodesic
Characterization of 9-Dimensional Anosov Lie Algebras
Journal of Lie theory, Tome 25 (2015) no. 3, pp. 857-873
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The classification of all real and rational Anosov Lie algebras up to dimension 8 was given by J. Lauret and C. E. Will [Nilmanifolds of dimension ≤ 8 admitting Anosov diffeomorphisms, Trans. Amer. Math. Soc. 361 (2009) 2377--2395]. In this paper we study 9-dimensional Anosov Lie algebras by using the properties of very special algebraic numbers and Lie algebra classification tools. We prove that there exists a unique, up to isomorphism, complex 3-step Anosov Lie algebra of dimension 9. In the 2-step case, we prove that a 2-step 9-dimensional Anosov Lie algebra with no abelian factor must have a 3-dimensional derived algebra and we characterize these Lie algebras in terms of their Pfaffian forms. Among these Lie algebras, we exhibit a family of infinitely many complex non-isomorphic Anosov Lie algebras.
Classification : 22E25, 37D20, 20F34
Mots-clés : Anosov Lie algebras, nilmanifolds, nilpotent Lie algebras, hyperbolic automorphisms 
@article{JLT_2015_25_3_JLT_2015_25_3_a10,
     author = {M. Mainkar and C. E. Will},
     title = {Characterization of {9-Dimensional} {Anosov} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {857--873},
     year = {2015},
     volume = {25},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a10/}
}
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M. Mainkar; C. E. Will. Characterization of 9-Dimensional Anosov Lie Algebras. Journal of Lie theory, Tome 25 (2015) no. 3, pp. 857-873. http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a10/