arXiv research

Study Einstein Lie groups and geodesic orbit manifolds, finding some are not geodesic orbit.

Let G/H be a strongly regular homogeneous space such that H is a Lie group of inner type. We show that G/H admits a proper action of a discrete non-virtually abelian subgroup of G if and only if G/H admits a proper action of a subgroup L of G locally isomorphic to SL(2,R). We classify all such spaces.

New subgroup found in Lie groups with unusual properties.

New Lie groups found for Poisson diffeomorphisms.

We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular infinite-dimensional Lie group, modelled on a locally convex strict inductive limit of Banach spa…

Constructs flows on quotients of Lie groups for Anosov subgroups.

We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By this criterion, we determine all the proper biharmonic submanifolds in irreducibl…

This paper classifies geodesic orbit metrics on compact Lie group $G_2$.

In this article we investigate a monoid of smooth mappings on the space of arrows of a Lie groupoid and its group of units. The group of units turns out to be an infinite-dimensional Lie group which is regular in the sense of Milnor. Furthermore, this group is closely connected to the group of bisections of the Lie gro…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie subgroups, and integrability of Lie algebra extensions to Lie group extensions. We furthe…

Study on subgroups' evolution in 3D Lie groups using mean curvature flow.

The study examines discrete subgroups of Lie groups and their residual finiteness.

Example found of subgroup not a lattice in product of Lie groups

The paper studies Riemannian metrics on Lie groups with specific commutator subgroups.

In this article, we give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of Lie groups defined by T.Robart [13], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem…

Cohomology of Lie group quotient equals Lie algebra cohomology.

Improved homological dimension for certain subgroups in Lie groups.

We discuss a Moser type argument to show when a deformation of a Lie group homomorphism and of a Lie subgroup is trivial. For compact groups we obtain stability results.

The study finds discrete subgroups with full limit sets in higher rank Lie groups.

Characterizes knotted subgroups of Lie groups and provides examples.

The paper finds free semigroups in dense subgroups of Lie groups with critical exponents arbitrarily close to the subgroup's.

Study on geometry and dynamics of transverse subgroups.

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the cor…

Study of Hermitian structures on Lie groups with 2D commutator subgroups.

The paper constructs Anosov representations for specific types of groups.

Characterizes isolated compact subgroups in Lie groups.

This paper classifies Ricci soliton subgroups in a specific type of nilpotent group.

Study answers arithmeticity question for normal subgroup of lattices.

In this article we classify all connected H-irreducible Lie subgroups of Sp(1,n) up to conjugacy.

It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are discussed as far as they carry.

Study uses Lie group subgroups to identify special subspaces in calibrations.

Researchers found sub-Lorentzian geodesics on a specific Lie subgroup.

Regular subgroups of SL3(R) are identified and ruled out.

Book on infinite-dimensional Lie groups, covering basics and various classes.

Study critical exponents in normal subgroups of higher rank Lie groups.

Let $p$ be an odd regular prime, and let $G_p$ denote the extraspecial $p$--group of order $p^{3}$ and exponent $p$. We show that $G_p$ acts freely and smoothly on $S^{2p-1} \times S^{2p-1}$. For $p=3$ we explicitly construct a free smooth action of a Lie group $\widetilde{G}_3$ containing $G_3$ on $S^{5} \times S^{5}$…

The study extends Dehn filling to Lie groups, ensuring geometric properties.

Reduces field theories on principal bundles by a subgroup, deriving reduced equations.

Survey on Coxeter groups for Lie group examples.

This paper classifies Ricci solitons in complex hyperbolic spaces.

Study Riemann-Finsler geometry on tangent bundles of Lie groups with 2D commutator subgroup.

We are interested in the class, in the Elie Cartan sense, of left invariant forms on a Lie group. We construct the class of Lie algebras provided with a contact form and classify the frobeniusian Lie algebras up to a contraction. We also study forms which are invariant by a subgroup. We show that the simple group SL(2n…

We develop the structure theory of symplectic Lie groups based on the study of their isotropic normal subgroups. The article consists of three main parts. In the first part we show that every symplectic Lie group admits a sequence of subsequent symplectic reductions to a unique irreducible symplectic Lie group. The sec…

Classifies Ricci soliton subgroups in specific Lie groups.

Study homogeneous Lorentzian manifolds under reductive Lie groups, reducing descriptions to semisimple groups.

The Greenberg-Shalom hypothesis connects subgroup properties to lattice structures in Lie groups.

No exact G₂-structures on compact Lie group quotients.

Study conformal foliations on Lie groups, finding new families and harmonic morphisms.