Infinite-dimensional Lie groups

This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. The author treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups, and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras.