On a diffeological group realization of certain generalized symmetrizable Kac-Moody Lie algebras.
On Analytic Vectors for Unitary Representations of Infinite Dimensional Lie Groups
Let be a connected and simply connected Banach–Lie group. On the complex enveloping algebra of its Lie algebra we define the concept of an analytic functional and show that every positive analytic functional is integrable in the sense that it is of the form for an analytic vector of a unitary representation of . On the way to this result we derive criteria for the integrability of -representations of infinite dimensional Lie algebras of unbounded operators to unitary group representations.For...
On formal theory of differential equations. III.
Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy...
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...