Dani, S. G. ; Mainkar, Meera G. (2004) Anosov automorphisms on compact nilmanifolds associated with graphs Transactions of the American Mathematical Society, 357 (6). pp. 22352251. ISSN 00029947

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Official URL: http://www.ams.org/journals/tran/200535706/S0002...
Abstract
We associate with each graph (S,E) a 2step simply connected nilpotent Lie group N and a lattice Γ in N. We determine the group of Lie automorphisms of N and apply the result to describe a necessary and sufficient condition, in terms of the graph, for the compact nilmanifold N/Γ to admit an Anosov automorphism. Using the criterion we obtain new examples of compact nilmanifolds admitting Anosov automorphisms, and conclude that for every n≥17 there exist a ndimensional 2step simply connected nilpotent Lie group N which is indecomposable (not a direct product of lower dimensional nilpotent Lie groups), and a lattice Γ in N such that N/Γ admits an Anosov automorphism; we give also a lower bound on the number of mutually nonisomorphic Lie groups N of a given dimension, satisfying the condition. Necessary and sufficient conditions are also described for a compact nilmanifold as above to admit ergodic automorphisms.
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Deposited On:  16 Dec 2011 09:25 
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