A Cartan decomposition for p-adic loop groups.
A characterization of coboundary Poisson Lie groups and Hopf algebras
We show that a Poisson Lie group (G,π) is coboundary if and only if the natural action of G×G on M=G is a Poisson action for an appropriate Poisson structure on M (the structure turns out to be the well known ). We analyze the same condition in the context of Hopf algebras. A quantum analogue of the structure on SU(N) is described in terms of generators and relations as an example.
A Lie Group Structure for Fourier Integral Operators.
A Lie Group Structure on the Space of Time-dependent Vector Fields.
A manifold structure for analytic isotropy Lie pseudogroups of infinite type.
A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus.
A structure theorem Lie algebras of unbounded derivations in -algebras
A survey on representations of the unitary group U(∞)
A unitarization process for some-locally compact topological groups.
Actions of some infinite Lie groups.
Algebraic characterizations of the algebra of functions and of the Lie algebra of vector fields of a manifold
Algebras whose groups of units are Lie groups
Let A be a locally convex, unital topological algebra whose group of units is open and such that inversion is continuous. Then inversion is analytic, and thus is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then has a locally diffeomorphic exponential function and multiplication is given locally by the Baker-Campbell-Hausdorff series. In contrast, for suitable non-Mackey complete A, the unit group is an analytic Lie group without...
Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Applications exponentielles pour les groupes des courants et la décomposition de Birkhoff pour les groupes des nœuds [Book]
Asymptotic products and enlargibility of Banach-Lie algebras.
Banach-Lie algebras of compact operators
Calculus of flows on convenient manifolds.
Calculus of flows on convenient manifolds
The study of diffeomorphism group actions requires methods of infinite dimensional analysis. Really convenient tools can be found in the Frölicher - Kriegl - Michor differentiation theory and its geometrical aspects. In terms of it we develop the calculus of various types of one parameter diffeomorphism groups in infinite dimensional spaces with smooth structure. Some spectral properties of the derivative of exponential mapping for manifolds are given.
Central extensions of infinite-dimensional Lie groups
The main result of the present paper is an exact sequence which describes the group of central extensions of a connected infinite-dimensional Lie group by an abelian group whose identity component is a quotient of a vector space by a discrete subgroup. A major point of this result is that it is not restricted to smoothly paracompact groups and hence applies in particular to all Banach- and Fréchet-Lie groups. The exact sequence encodes in particular precise obstructions for a given Lie algebra...
Closed subgroups of nuclear spaces are weakly closed