Non-abelian extensions have nonsimple spectrum

E. Arthur Robinson

Compositio Mathematica (1988)

  • Volume: 65, Issue: 2, page 155-170
  • ISSN: 0010-437X

How to cite

top

Robinson, E. Arthur. "Non-abelian extensions have nonsimple spectrum." Compositio Mathematica 65.2 (1988): 155-170. <http://eudml.org/doc/89886>.

@article{Robinson1988,
author = {Robinson, E. Arthur},
journal = {Compositio Mathematica},
keywords = {group extension; ergodic measure preserving transformations; maximal spectral multiplicity; non-simple spectrum; Abelian extensions},
language = {eng},
number = {2},
pages = {155-170},
publisher = {Kluwer Academic Publishers},
title = {Non-abelian extensions have nonsimple spectrum},
url = {http://eudml.org/doc/89886},
volume = {65},
year = {1988},
}

TY - JOUR
AU - Robinson, E. Arthur
TI - Non-abelian extensions have nonsimple spectrum
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 65
IS - 2
SP - 155
EP - 170
LA - eng
KW - group extension; ergodic measure preserving transformations; maximal spectral multiplicity; non-simple spectrum; Abelian extensions
UR - http://eudml.org/doc/89886
ER -

References

top
  1. [BFK] M. Brin, J. Feldman and A. Katok, Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents, Annals of Math.113 (1981) 159-179. Zbl0477.58021MR604045
  2. [C] R. Chacon, Approximation and spectral multiplicity, Lect. Notes in Math.160 (1970) 18-22. Zbl0212.40101MR271303
  3. [Fu] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math.83 (1961) 573-601. Zbl0178.38404MR133429
  4. [G] G. Goodson, On the spectral multiplicity of a class of finite rank transformations, Proc. Amer. Math. Soc.93 (1985) 303-306. Zbl0551.28019MR770541
  5. [J] A. del Junco, A transformation with simple spectrum which is not rank one, Can. J. Math.29 (1977) 655-663. Zbl0335.28010MR466489
  6. [K] A. Katok, Constructions in Ergodic Theory. Progress in Mathematics, Burkhauser, Boston (to appear). Zbl1030.37001MR1858535
  7. [KS] A. Katok and A. Stepin, Approximations in ergodic theory, Uspekhi Mat. Nuak.22 (1967); Russian Math. Surveys22 (1967) 77-102. Zbl0172.07202MR219697
  8. [Ki] J. King, The comutant in the weak closure of the powers for rank-1 transformations, Ergod. Th. and Dynam. Sys. 6 (1986) 363-384. Zbl0595.47005MR863200
  9. [M1] G. Mackey, Unitary Group Representations in Physics, Probability and Number Theory, Benjamin/Cummings, Reading, MA (1978). Zbl0401.22001MR515581
  10. [M2] G. Mackey, Induced Representations of Groups and Quantum Mechanics, W.A. Benjamin, New York (1968). Zbl0174.28101MR507212
  11. [MwN] J. Mathew and M. Nadkarni, A measure preserving transformation whose spectrum has a Lebesgue component of multiplicity two, Bull. London Math. Soc.16 (1984) 402-406. Zbl0515.28010MR749448
  12. [Mo] C. Moore, Groups with finite dimensional irreducible representations, Trans. Amer. Math. Soc.166 (1972) 401-410. Zbl0236.22010MR302817
  13. [O] V. Oseledec, The spectrum of ergodic automorphisms, Dokl. Akad. Nuak SSSR168 (1966) 402-406. Zbl0152.33404MR199347
  14. [P] W. Parry, Ergodic properties of transformations and flows on nilmanifolds, Amer. J. Math.91 (1969) 757-771. Zbl0183.51503MR260975
  15. [R1] A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Inv. Math.72 (1983) 229-314. Zbl0519.28008MR700773
  16. [R2] A. Robinson, Mixing and spectral multiplicity, Ergod. Th. and Dynam. Sys. 5 (1985) 617-624. Zbl0565.28013MR829862
  17. [R3] A. Robinson, Transformations with highly nonhomogeneous spectrum of finite multiplicity, Israel J. Math.56 (1986) 75-88. Zbl0614.28012MR879915
  18. [R4] A. Robinson, Ergodic properties that lift to compact abelian extensions, Proc. Amer. Math. Soc.101 (1987) (to appear). Zbl0636.28007MR915717
  19. [Ru1] D. Rudolph, k-Fold mixing lifts to weakly mixing isometric extensions, Ergod. Th. and Dynam. Sys.5 (1985) 445-447. Zbl0594.28015MR805841
  20. [Ru2] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, J. D'Analyse. Math.34 (1978) 36-60. Zbl0415.28012MR531270
  21. [V] W. Veech, Finite group extensions of irrational rotations, Israel J. Math.21 (1975) 240-259. Zbl0334.28014MR396913

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.