# Isometric extensions, 2-cocycles and ergodicity of skew products

Alexandre Danilenko; Mariusz Lemańczyk

Studia Mathematica (1999)

- Volume: 137, Issue: 2, page 123-142
- ISSN: 0039-3223

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topDanilenko, Alexandre, and Lemańczyk, Mariusz. "Isometric extensions, 2-cocycles and ergodicity of skew products." Studia Mathematica 137.2 (1999): 123-142. <http://eudml.org/doc/216679>.

@article{Danilenko1999,

abstract = {We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension $T_α$ and admits a prescribed subgroup in the centralizer of $T_α$.},

author = {Danilenko, Alexandre, Lemańczyk, Mariusz},

journal = {Studia Mathematica},

keywords = {ergodic transformation; cocycle; isometric extension; nonsingular transformation; centralizer; ergodicity},

language = {eng},

number = {2},

pages = {123-142},

title = {Isometric extensions, 2-cocycles and ergodicity of skew products},

url = {http://eudml.org/doc/216679},

volume = {137},

year = {1999},

}

TY - JOUR

AU - Danilenko, Alexandre

AU - Lemańczyk, Mariusz

TI - Isometric extensions, 2-cocycles and ergodicity of skew products

JO - Studia Mathematica

PY - 1999

VL - 137

IS - 2

SP - 123

EP - 142

AB - We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension $T_α$ and admits a prescribed subgroup in the centralizer of $T_α$.

LA - eng

KW - ergodic transformation; cocycle; isometric extension; nonsingular transformation; centralizer; ergodicity

UR - http://eudml.org/doc/216679

ER -

## References

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