On groups of smooth maps into a simple compact Lie group.
On infinite Lie groups
Under some regularity conditions one proves that quotients and kernels of infinitesimal analytic Lie pseudo-groups by invariant fiberings are again infinitesimal Lie pseudo-groups. The regularity conditions are shown to be necessary and sufficient if one wishes both quotient and kernel to be infinitesimal Lie pseudo-groups. One defines and proves the existence of the quotient of an infinitesimal Lie pseudo-group by a normal sub-pseudo group. An equivalence relation for germs of infinitesimal Lie...
On the existence of commutative Banach-Lie groups which do not admit continuous unitary representations
On the Existence of Exotic Banach-Lie Groups.
On the existence of unitary representations of commutative nuclear Lie groups
On the geometry of the Virasoro-Bott group.
On the irreducibility and inequivalence of unitary representations of gauge groups
On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds
The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.
On universal enveloping algebras in a topological setting
We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups...
One-parameter subgroups and the B-C-H formula
An algebraic scheme for Lie theory of topological groups with "large" families of one-parameter subgroups is proposed. Such groups are quotients of "𝔼ℝ-groups", i.e. topological groups equipped additionally with the continuous exterior binary operation of multiplication by real numbers, and generated by special ("exponential") elements. It is proved that under natural conditions on the topology of an 𝔼ℝ-group its group multiplication is described by the B-C-H formula in terms of the associated...
Potential Theory on the Infinite Dimensional Torus.
Prescribed Gauss decompositions for Kac-Moody groups over fields
Projective limits of Banach vector bundles.
Quantization and irreducible representations of infinite-dimensional transformation groups and Lie algebras.
Quasi-bigèbres jacobiennes
Reduction of Hamiltonian Systems, Affine Lie Algebras and Lax Equations.
Regular infinite dimensional Lie groups.
Regular Lie groups and a theorem of Lie-Palais.
Remarque sur la cohomologie de l'algèbre de Lie des champs de vecteurs sur la sphère
Representations of the group of functions taking values in a compact Lie group