1Dept. of Mathematics, Pearce Hall, Central Michigan University, Mt. Pleasant, MI 48859, U.S.A. 2FaMAF and CIEM, Universidad Nacional de Córdoba, Haya de la Torre s/n, 5000 Córdoba, Argentina
Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 857-873
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.
1
Dept. of Mathematics, Pearce Hall, Central Michigan University, Mt. Pleasant, MI 48859, U.S.A.
2
FaMAF and CIEM, Universidad Nacional de Córdoba, Haya de la Torre s/n, 5000 Córdoba, Argentina
Meera Mainkar; Cynthia 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/JOLT_2015_25_3_a10/
@article{JOLT_2015_25_3_a10,
author = {Meera Mainkar and Cynthia 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/JOLT_2015_25_3_a10/}
}
TY - JOUR
AU - Meera Mainkar
AU - Cynthia E. Will
TI - Characterization of 9-Dimensional Anosov Lie Algebras
JO - Journal of Lie Theory
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