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Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses

Published online by Cambridge University Press:  20 November 2018

J. P. Henniger
J. P. Henniger*
Affiliation:
Department of Mathematics Trent University Peterborough, Ontario K9J 7B8, email: [email protected]
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Abstract

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In answer to a question posed in [3], we give sufficient conditions on a Lie nilmanifold so that any ergodic rotation of the nilmanifold is metrically conjugate to its inverse. The condition is that the Lie algebra be what we call quasi-graded, and is weaker than the property of being graded. Furthermore, the conjugating map can be chosen to be an involution. It is shown that for a special class of groups, the condition of quasi-graded is also necessary. In certain examples there is a continuum of conjugacies.

Keywords

28Dxx22E25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 4 , 01 December 2001 , pp. 429 - 439
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] Auslander, L., Green, L. and Hahn, F., Flows on homogeneous spaces. Ann. of Math. Stud. 53, Princeton, 1963.Google Scholar
[2] Corwin, L. and Greenleaf, F. P., Representations of nilpotent Lie groups and their applications Part 1: Basic Theory and examples. Cambridge University Press, Cambridge, 1990.Google Scholar
[3] Goodson, G., del Junco, A., Lemanczyk, M. and Rudolph, D., Ergodic transformations conjugate to their inverses by involutions. Ergodic Theory Dynamical Systems 16 (1996), 97–124.Google Scholar
[4] Halmos, P. R., Ergodic Theory. Chelsea, New York, 1965.Google Scholar
[5] Hochschild, G., The Structure of Lie Groups. San Fransisco, Holden-Day, 1965.Google Scholar
[6] Malcev, A. I., On a class of homogeneous spaces. Amer.Math. Soc. Translation 39 (1951), 3–33; Isvest. Acad. Nauk. USSR, Ser.Mat. 13, 9–32.Google Scholar
[7] Parry, W., Metric classification of ergodic nilflows and unipotent affines. Amer. J. Math. 93 (1971), 819–828.Google Scholar
[8] Parry, W., Ergodic properties of affine transformations and flows on nilmanifolds. Amer. J. Math. 91 (1969), 757–771.Google Scholar