Non-commutative holomorphic semicocycles
Complex Variables
2019-10-07 v2
Abstract
This paper studies holomorphic semicocycles over semigroups in the unit disk, which take values in an arbitrary unital Banach algebra. We prove that every such semicocycle is a solution to a corresponding evolution problem. We then investigate the linearization problem: which semicocycles are cohomologous to constant semicocycles? In contrast with the case of commutative semicocycles, in the non-commutative case non-linearizable semicocycles are shown to exist. Simple conditions for linearizability are derived and are shown to be sharp.
Cite
@article{arxiv.1707.00245,
title = {Non-commutative holomorphic semicocycles},
author = {Mark Elin and Fiana Jacobzon and Guy Katriel},
journal= {arXiv preprint arXiv:1707.00245},
year = {2019}
}