Rafael de la Llave, Maria Saprykina
Nonconmutative coboundary equations over integrable systems
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ABSTRACT.  We prove an analog of Liv{s}ic theorem for real-analytic families of 
cocycles over an integrable system with values in a Banach algebra 
$\G$ 
or a Lie group. 
Namely, we consider an 
integrable dynamical system $f:\M quiv	orus^d 	imes [-1,1]^d	o 
\M$, $f(	heta, I)=(	heta + I, I)$, and a real-analytic family of 
cocycles $ta_ps : \M 	o \G$, indexed by a complex parameter $ps$ in an open ball $