On cocycle superrigidity for Gaussian actions

نویسندگان

  • JESSE PETERSON
  • THOMAS SINCLAIR
چکیده

We present a general setting to investigate Ufin-cocycle superrigidity for Gaussian actions in terms of closable derivations on von Neumann algebras. In this setting we give new proofs to some Ufin-cocycle superrigidity results of S. Popa and we produce new examples of this phenomenon. We also use a result of K. R. Parthasarathy and K. Schmidt to give a necessary cohomological condition on a group representation in order for the resulting Gaussian action to be Ufin-cocycle superrigid.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ar X iv : m at h / 03 03 23 6 v 1 [ m at h . D S ] 1 9 M ar 2 00 3 LOCAL RIGIDITY FOR COCYCLES

In this paper we study perturbations of constant co-cycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's co-cycle superrigidity theorems implies that the perturbed cocycle is measurably conjugate to a constant cocycle modulo a compact valued cocycle. The main point of this article is to see that a cocycle which is a c...

متن کامل

ar X iv : m at h / 03 03 23 6 v 3 [ m at h . D S ] 1 2 N ov 2 00 3 LOCAL RIGIDITY FOR COCYCLES

In this paper we study perturbations of constant co-cycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's co-cycle superrigidity theorems implies that the perturbed cocycle is measurably conjugate to a constant cocycle modulo a compact valued cocycle. The main point of this article is to see that a cocycle which is a c...

متن کامل

m at h . D S ] 1 5 A pr 2 00 3 LOCAL RIGIDITY FOR COCYCLES

In this paper we study perturbations of constant co-cycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's co-cycle superrigidity theorems implies that the perturbed cocycle is measurably conjugate to a constant cocycle modulo a compact valued cocycle. The main point of this article is to see that a cocycle which is a c...

متن کامل

2 00 4 Non - ergodic actions , cocycles and superrigidity

Abstract. This paper proves various results concerning non-ergodic actions of locally compact groups and particularly Borel cocycles defined over such actions. The general philosophy is to reduce the study of the cocycle to the study of its restriction to each ergodic component of the action, while being careful to show that all objects arising in the analysis depend measurably on the ergodic c...

متن کامل

Nonergodic actions, cocycles and superrigidity

This paper proves various results concerning nonergodic actions of locally compact groups and particularly Borel cocycles defined over such actions. The general philosophy is to reduce the study of the cocycle to the study of its restriction to each ergodic component of the action, while being careful to show that all objects arising in the analysis depend measurably on the ergodic component. T...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011