arXiv research

Study locally conformally balanced metrics on specific Lie algebras.

Study on CKY forms on almost abelian Lie groups, proving parallelism and characterizing non-parallel cases.

Study balanced Hermitian structures on almost abelian Lie algebras, classifying six-dimensional cases.

Study pseudo-Kähler structures on almost abelian solvmanifolds.

Study of presymplectic forms on almost abelian Lie algebras, determining moduli spaces and their finiteness.

Unique complex structures on specific Lie algebras.

This paper classifies LCSKT almost abelian Lie algebras in 6 dimensions.

Study of abelian structures on odd-dimensional Lie algebras and their geometric properties.

Characterizes almost abelian Lie algebras with integrable complex structure

The paper classifies hypercomplex Lie algebras and solvmanifolds using quaternionic Jordan form.

Study coKähler structures on Lie algebras using Fino-Vezzoni correspondence.

Paper confirms conjecture for specific Lie algebras.

Characterizes almost Abelian Lie algebras with special $H$-structures.

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

The paper constructs a new Ricci-flat metric on almost abelian Lie groups.

The paper studies a flow on complex Lie groups, showing convergence to solitons.

In this article, we determine the seven-dimensional almost Abelian Lie algebras which admit calibrated or parallel G_2-/G_2^*-structures. Along the way, we show that certain well-established curvature restrictions for calibrated and parallel G_2-structures are not valid in the G_2^* case. In more detail, we provide the…

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

Study characterizes $G_2$-structures on specific Lie groups and identifies harmonic conditions.

Harmonic almost complex structures on specific Lie groups and solvmanifolds identified.

Classifies two-step solvable Lie groups with SKT structures.

We construct lattices on six dimensional not completely solvable almost abelian Lie groups, for which the Mostow condition does not hold. For the corresponding compact quotients, we compute the de Rham cohomology (which does not agree in general with the Lie algebra one) and a minimal model. We show that some of these …

Abstract classifies Lie algebras with complex or symplectic structures.

The study examines weakly Einstein Lie groups and proves non-existence for certain types.

Study of complex and Hermitian structures on specific Lie groups.

Study on a specific type of Lie algebras with Kähler and contact properties.

The Streets-Tian conjecture is confirmed for Lie algebras with specific abelian ideals.

The note confirms a conjecture for specific Lie groups.

Characterizes hypercomplex Lie groups and their solvmanifolds.

Study of complex structures on specific solvmanifolds, proving existence and non-existence results.

The paper classifies invariant structures on complex almost Abelian groups.

Study abelian factors in Lie algebras from graph edge labels.

We consider higher dimensional generalisations of normal almost contact structures, the so called f.pk-structures where parallelism spans a Lie algebra g (f.pk-g-structures). Two types of these structures are discussed. In the first case, we construct an almost complex structure on a product manifold mirroring K-struct…

Study second-Chern-Einstein metrics on 4D manifolds, finding Killing vector fields and examples.

We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\frak a \frak f \frak f (A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural generalizations of $\frak a \frak f \frak f (\Bbb C)$ and the corresponding Lie grou…

The paper studies nice bases for Lie algebras and their properties.

Study on Hermitian metrics on Lie algebras with specific ideals.

The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented a generalization of the twist, a shear construction of rank one, which allowed …

Study on harmonic spinors on specific Lie groups.

The paper explores SKT, balanced, and generalized Kähler structures on specific Lie groups.

We construct an abelian quotient of the symplectic derivation Lie algebra $\mathfrak{h}_{g,1}$ of the free Lie algebra generated by the fundamental representation of $\mathrm{Sp}(2g,\mathbb{Q})$. More specifically, we show that the weight $12$ part of the abelianization of $\mathfrak{h}_{g,1}$ is $1$-dimensional for $g…

Classifies Lie symmetry algebras for 2D quasilinear equations, linking symmetry to linearity.

The study explores Lie superalgebras constructed from Lie algebras using Schouten-like brackets.

For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and non-existence results in certain cases: unimodular solvable Lie algebras having an abelian nilradical, algebras having an abelian derived algebra, algeb…

The aim of this note is to introduce the notion of a $\operatorname{D}$-Lie algebra and to prove some elementary properties of $\operatorname{D}$-Lie algebras, the category of $\operatorname{D}$-Lie algebras, the category of modules on a $\operatorname{D}$-Lie algebra and extensions of $\operatorname{D}$-Lie algebras. …

We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.

We introduce hom-Lie-Rinehart algebras as an algebraic analogue of hom-Lie algebroids, and systematically describe a cohomology complex by considering coefficient modules. We define the notion of extensions for hom-Lie-Rinehart algebras. In the sequel, we deduce a characterisation of low dimensional cohomology spaces i…

Characterizes symmetric Killing tensors on specific Lie groups.