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The Livsic Cocycle Equation for Compact Lie Group Extensions of Hyperbolic Systems
Author(s) -
Parry William,
Pollicott Mark
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610797005474
Subject(s) - mathematics , lie group , pure mathematics , group (periodic table) , constant (computer programming) , simple lie group , algebra over a field , computer science , physics , quantum mechanics , programming language
In this article we extend well‐known results of Livsic on the regularity of measurable solutions to the cocycle equation. Livsic proved a regularity result for real valued cocycles, but for compact Lie group valued cocycles his result was restricted to coboundaries (that is, trivial or constant cocycles). In this article we prove the complete result. We present several useful applications of these results.