@unpublished{64629, author = {{Glöckner, Helge and Neeb, Karl-Hermann}}, pages = {{1056}}, title = {{{Infinite-dimensional Lie groups}}}, year = {{2026}}, } @unpublished{65036, author = {{Cohen, Tal and Glöckner, Helge and Goffer, Gil and Lederle, Waltraud}}, title = {{{Compact invariant random subgroups}}}, year = {{2026}}, } @article{63649, author = {{Glöckner, Helge and Schmeding, Alexander and Suri, Ali}}, issn = {{2972-4589}}, journal = {{Geometric Mechanics}}, number = {{04}}, pages = {{383--437}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Manifolds of continuous BV-functions and vector measure regularity of Banach–Lie groups}}}, doi = {{10.1142/s2972458925500029}}, volume = {{01}}, year = {{2025}}, } @misc{64736, booktitle = {{J. Lie Theory}}, editor = {{Frahm, Jan and Glöckner, Helge and Hilgert, Joachim and Olafsson, Gestur}}, number = {{4}}, title = {{{Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}}}, volume = {{35}}, year = {{2025}}, } @article{34807, abstract = {{Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all real-analytic diffeomorphisms of $M$, which is modelled on the (DFS)-space ${\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of time-dependent real-analytic vector fields on $M$ which are integrable functions in time, and their dependence on the time-dependent vector field. Notably, we show that the Lie group $G$ is $L^1$-regular in the sense that each $[\gamma]$ in $L^1([0,1],{\mathfrak g})$ has an evolution which is an absolutely continuous $G$-valued function on $[0,1]$ and smooth in $[\gamma]$. As tools for the proof, we develop several new results concerning $L^p$-regularity of infinite-dimensional Lie groups, for $1\leq p\leq \infty$, which will be useful also for the discussion of other classes of groups. Moreover, we obtain new results concerning the continuity and complex analyticity of non-linear mappings on open subsets of locally convex direct limits.}}, author = {{Glöckner, Helge}}, journal = {{Nonlinear Analysis}}, title = {{{Lie groups of real analytic diffeomorphisms are L^1-regular}}}, doi = {{10.1016/j.na.2024.113690}}, volume = {{252}}, year = {{2025}}, } @unpublished{56116, author = {{Glöckner, Helge and Grong, Erlend and Schmeding, Alexander}}, title = {{{Boundary values of diffeomorphisms of simple polytopes, and controllability}}}, year = {{2024}}, } @unpublished{56583, author = {{Glöckner, Helge and Suri, Ali}}, title = {{{L^1-regularity of strong ILB-Lie groups}}}, year = {{2024}}, } @article{34793, author = {{Glöckner, Helge and Hilgert, Joachim}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{22E65, 28B05, 34A12, 34H05, 46E30, 46E40}}, pages = {{186–232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, doi = {{10.1016/j.jde.2022.10.001}}, volume = {{343}}, year = {{2023}}, } @article{34803, author = {{Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}}, journal = {{BIT Numerical Mathematics}}, publisher = {{Springer}}, title = {{{Deep neural networks on diffeomorphism groups for optimal shape reparametrization}}}, doi = {{10.1007/s10543-023-00989-05}}, volume = {{63}}, year = {{2023}}, } @article{34805, abstract = {{Let $E$ be a finite-dimensional real vector space and $M\subseteq E$ be a convex polytope with non-empty interior. We turn the group of all $C^\infty$-diffeomorphisms of $M$ into a regular Lie group.}}, author = {{Glöckner, Helge}}, journal = {{Journal of Convex Analysis}}, number = {{1}}, pages = {{343--358}}, publisher = {{Heldermann}}, title = {{{Diffeomorphism groups of convex polytopes}}}, volume = {{30}}, year = {{2023}}, } @article{34801, author = {{Glöckner, Helge and Tárrega, Luis}}, journal = {{Journal of Lie Theory}}, number = {{1}}, pages = {{271--296}}, publisher = {{Heldermann}}, title = {{{Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }}}, volume = {{33}}, year = {{2023}}, } @article{34792, author = {{Glöckner, Helge}}, issn = {{2070-0466}}, journal = {{p-Adic Numbers, Ultrametric Analysis, and Applications}}, keywords = {{20Exx, 22Exx, 32Cxx}}, number = {{2}}, pages = {{138–144}}, title = {{{Non-Lie subgroups in Lie groups over local fields of positive characteristic}}}, doi = {{10.1134/S2070046622020042}}, volume = {{14}}, year = {{2022}}, } @article{34791, author = {{Glöckner, Helge and Schmeding, Alexander}}, issn = {{0232-704X}}, journal = {{Annals of Global Analysis and Geometry}}, keywords = {{58D15, 22E65, 26E15, 26E20, 46E40, 46T20, 58A05}}, number = {{2}}, pages = {{359–398}}, title = {{{Manifolds of mappings on Cartesian products}}}, doi = {{10.1007/s10455-021-09816-y}}, volume = {{61}}, year = {{2022}}, } @article{34796, abstract = {{We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E×E is a kR-space.}}, author = {{Glöckner, Helge}}, issn = {{2075-1680}}, journal = {{Axioms}}, number = {{5}}, title = {{{Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}}}, doi = {{10.3390/axioms11050221}}, volume = {{11}}, year = {{2022}}, } @unpublished{34804, abstract = {{Starting with a finite-dimensional complex Lie algebra, we extend scalars using suitable commutative topological algebras. We study Birkhoff decompositions for the corresponding loop groups. Some results remain valid for loop groups with valued in complex Banach-Lie groups.}}, author = {{Glöckner, Helge}}, booktitle = {{arXiv:2206.11711}}, title = {{{Birkhoff decompositions for loop groups with coefficient algebras}}}, year = {{2022}}, } @article{34786, abstract = {{A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups.}}, author = {{Glöckner, Helge and Willis, George A.}}, issn = {{0021-8693}}, journal = {{Journal of Algebra}}, keywords = {{Contraction group, Torsion group, Extension, Cocycle, Section, Equivariant cohomology, Abelian group, Nilpotent group, Isomorphism types}}, pages = {{164--214}}, title = {{{Decompositions of locally compact contraction groups, series and extensions}}}, doi = {{https://doi.org/10.1016/j.jalgebra.2020.11.007}}, volume = {{570}}, year = {{2021}}, } @article{34795, author = {{Glöckner, Helge}}, issn = {{0025-584X}}, journal = {{Mathematische Nachrichten}}, number = {{1}}, pages = {{74–81}}, title = {{{Direct limits of regular Lie groups}}}, doi = {{10.1002/mana.201900073}}, volume = {{294}}, year = {{2021}}, } @unpublished{34806, abstract = {{Let $G$ be a Lie group over a totally disconnected local field and $\alpha$ be an analytic endomorphism of $G$. The contraction group of $\alpha$ ist the set of all $x\in G$ such that $\alpha^n(x)\to e$ as $n\to\infty$. Call sequence $(x_{-n})_{n\geq 0}$ in $G$ an $\alpha$-regressive trajectory for $x\in G$ if $\alpha(x_{-n})=x_{-n+1}$ for all $n\geq 1$ and $x_0=x$. The anti-contraction group of $\alpha$ is the set of all $x\in G$ admitting an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $x_{-n}\to e$ as $n\to\infty$. The Levi subgroup is the set of all $x\in G$ whose $\alpha$-orbit is relatively compact, and such that $x$ admits an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $\{x_{-n}\colon n\geq 0\}$ is relatively compact. The big cell associated to $\alpha$ is the set $\Omega$ of all all products $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and $z$ in the anti-contraction group. Let $\pi$ be the mapping from the cartesian product of the contraction group, Levi subgroup and anti-contraction group to $\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\Omega$ is open in $G$ and $\pi$ is \'{e}tale for suitable immersed Lie subgroup structures on the three subgroups just mentioned. Moreover, we study group-theoretic properties of contraction groups and anti-contraction groups.}}, author = {{Glöckner, Helge}}, booktitle = {{arXiv:2101.02981}}, title = {{{Contraction groups and the big cell for endomorphisms of Lie groups over local fields}}}, year = {{2021}}, } @article{34790, author = {{Glöckner, Helge and Willis, George A.}}, issn = {{0075-4102}}, journal = {{Journal für die reine und angewandte Mathematik}}, keywords = {{22D05, 22A05, 20E18}}, pages = {{85–103}}, title = {{{Locally pro-p contraction groups are nilpotent}}}, doi = {{10.1515/crelle-2021-0050}}, volume = {{781}}, year = {{2021}}, } @article{34789, author = {{Amiri, Habib and Glöckner, Helge and Schmeding, Alexander}}, issn = {{0044-8753}}, journal = {{Archivum Mathematicum}}, keywords = {{22A22, 22E65, 22E67, 46T10, 47H30, 58D15, 58H05}}, number = {{5}}, pages = {{307–356}}, title = {{{Lie groupoids of mappings taking values in a Lie groupoid}}}, doi = {{10.5817/AM2020-5-307}}, volume = {{56}}, year = {{2020}}, }