Title: Free Banach-Lie algebras, couniversal Banach-Lie groups, and more
Abstract:The construction of free Banach-Lie algebra over a normed space enables us to build a connected separable Banach-Lie group of which any other connected separable Banach-Lie group is a quotient.New pro...The construction of free Banach-Lie algebra over a normed space enables us to build a connected separable Banach-Lie group of which any other connected separable Banach-Lie group is a quotient.New proofs are given to the result on representability of any Banach-Lie algebra as a quotient of an enlargable Banach-Lie algebra (due to van Est and Swierczkowski) and to the result on representability of any topological group as a quotient of a group with no small subgroups (due to successive efforts of Morris and Thompson, the author, and Sipacheva and Uspenskiϊ).Read More