
Journal of Lie Theory 25 (2015), No. 3, 857873 Copyright Heldermann Verlag 2015 Characterization of 9Dimensional Anosov Lie Algebras Meera Mainkar Dept. of Mathematics, Pearce Hall, Central Michigan University, Mt. Pleasant, MI 48859, U.S.A. maink1m@cmich.edu Cynthia E. Will FaMAF and CIEM, Universidad Nacional de Córdoba, Haya de la Torre s/n, 5000 Córdoba, Argentina cwill@famaf.unc.edu.ar 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) 23772395]. In this paper we study 9dimensional 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 3step Anosov Lie algebra of dimension 9. In the 2step case, we prove that a 2step 9dimensional Anosov Lie algebra with no abelian factor must have a 3dimensional 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 nonisomorphic Anosov Lie algebras. Keywords: Anosov Lie algebras, nilmanifolds, nilpotent Lie algebras, hyperbolic automorphisms. MSC: 22E25; 37D20, 20F34 [ Fulltextpdf (297 KB)] for subscribers only. 