Characterization of 9-dimensional Anosov Lie algebras

Meera Mainkar, Cynthia E. Will

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The classification of all real and rational Anosov Lie algebras up to dimension 8 is given by Lauret and Will. 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.

Original languageEnglish
Pages (from-to)857-873
Number of pages17
JournalJournal of Lie Theory
Issue number3
StatePublished - 2015


  • Anosov Lie algebras
  • Hyperbolic automorphisms
  • Nilmanifolds
  • Nilpotent lie algebras


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