arXiv research

No exact G₂-structures on compact Lie group quotients.

Lie algebras of quotient groups defined under specific conditions.

New findings on how foliations and Lie group actions interact.

Balanced metrics found on Lie groups and their quotients.

New manifold types defined on quotient spaces.

The paper explores $p$-Kähler structures on Lie group quotients.

In this paper we show that every invariant Finsler metric on Lie group $G$, induces an invariant Finsler metric on quotient group $G/H$ in the natural way, where $H$ is a closed normal Lie subgroup of $G$.

Study Dolbeault harmonic forms on Lie group quotients with specific structures.

The paper explores mapping class group quotients by Dehn twists and their representations.

Uniform doubling property proven for specific Lie groups.

It is shown that every abelian regular Lie group is a quotient of its Lie algebra via the exponential mapping.

The paper defines conditions for a Riemannian structure on a symplectic quotient.

Study compact symplectic solvmanifolds' hard Lefschetz property.

In this paper we apply the hyper-Kähler quotient construction to Lie groups with a left invariant hyper-Kähler structure under the action of a closed abelian subgroup by left multiplication. This is motivated by the fact that some known hyper-Kähler metrics can be recovered in this way by considering different Lie grou…

We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group $G$ on a Poisson manifold $M$, we find an explicit description of the lifted hamiltonian act…

Study Weyl-Einstein structures on conformal solvmanifolds, proving Einstein property and classifying metrics.

By means of cohomology groups, we study relationships between equivariant gerbes with connection over a manifold with a Lie group action and gerbes with connection over the quotient space.

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and investigate properties of the corresponding representations. We obtain some structural …

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie groups which are locally isomorphic to $N$ and a union of certain quotients of noncom…

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our method to construct many examples of compact minimal submanifolds of the special u…

Study integrability in Poisson and Dirac structures from quotients.

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses a question of K. Grove's about Riemannian submersions from Lie groups.

Cohomology of Lie group quotient equals Lie algebra cohomology.

We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group $H_{2n + 1}$. Furthermore, we classify Sasakian Lie algebras of dimension 5 and determine which of th…

Geometric compactification for complex structures on Lie groups.

Unified product Lie groups and their quotient spaces are analyzed for dynamics.

We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we show that these structures provide solutions of supersymmetric equations of type IIA.

Researchers show how complex structures vary in symplectic quotients.

Local norms of Fourier multipliers bounded on discrete subgroups of Lie groups.

We generalize the hyperkaehler quotient construction to the situation where there is no group action preserving the hyperkaehler structure but for each complex structure there is an action of a complex group preserving the corresponding complex symplectic structure. Many (known and new) hyperkaehler manifolds arise as …

Study controllability of diffeomorphisms of simple polytopes.

Classifies complex symplectic structures on Lie algebras with large abelian ideals.

We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras integrates to a corresponding Lie group extension $\hat{G}$ of $G$ by $A$, where $G$ is a connected, simply connected Lie group and $A$ is a quotient of its Lie algebra by some discrete subgroup. When $G$ is non-simply connected…

Improved homological dimension for certain subgroups in Lie groups.

Characterizes metrics on Lie groups, proving non-simultaneous existence of balanced and pluriclosed metrics.

Using canonical 1-parameter family of Hermitian connections on the tangent bundle, we provide invariant solutions to the Strominger system on complex Lie groups. Both flat and non-flat cases are discussed in detail.

The paper shows commensurators of certain subgroups are discrete.

The study explores deformations of discrete subgroups in non-compact homogeneous spaces.

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients of all four-dimensional connected and simply connected solvable Lie groups.

The study integrates Banach manifolds into H-manifolds, integrating Lie algebras into H-groups.

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $[M/G]$, where $M$ is a smooth manifold equipped with a smooth proper action by a Lie group $G$. The characterization is described in terms of the action of the connected componen…

Study on CR structures on 3D Lie groups, focusing on equivalence and closed chains.

Constructs flows on quotients of Lie groups for Anosov subgroups.

Defines super stable maps and proves quotient superorbifolds for genus zero.

Locally conformal SKT structures are introduced and studied on Lie groups and their compact quotients.

The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangi…

Let K be a compact Lie group. We compute the abelianization of the Lie algebra of equivariant vector fields on a smooth K-manifold X. We also compute the abelianization of the Lie algebra of strata preserving smooth vector fields on the quotient X/K.

We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry…