A double Ore extension was introduced by James Zhang and Jun Zhang \cite{ZhZh} to study Artin-Schelter regular algebras. Here we give a definition of double Poisson extension which may be considered as a Poisson analogue of double Ore extension and show that algebras in a class of double Ore extensions are deformations of double Poisson extensions. We also investigate the relationship between double Poisson extensions and iterated Poisson polynomial extensions. Results are illustrated by examples. 查看全文>>