Related papers: Local Type I Metrics with Holonomy in ${\rm G}_{2}…

Let $M$ be a simply connected pseudo-Riemannian homogeneous space of finite volume with isometry group $G$. We show that $M$ is compact and that the solvable radical of $G$ is abelian and the Levi factor is a compact semisimple Lie group…

Every Lie algebra over a field $E$ gives rise to new Lie algebras over any subfield $F \subseteq E$ by restricting the scalar multiplication. This paper studies the structure of these underlying Lie algebra in relation to the structure of…

An algebra $L$ over a field $\Bbb F$, in which product is denoted by $[\,,\,]$, is said to be \textit{ Lie type algebra} if for all elements $a,b,c\in L$ there exist $\alpha, \beta\in \Bbb F$ such that $\alpha\neq 0$ and $[[a,b],c]=\alpha…

We present a classification of all spherical indecomposable representations of classical and exceptional Lie superalgebras. We also include information about stabilizers, symmetric algebras, and Borels for which sphericity is achieved. In…

A complex hyperplane arrangement $\mathcal{A}$ is said to be decomposable if there are no elements in the degree 3 part of its holonomy Lie algebra besides those coming from the rank 2 flats. When this purely combinatorial condition is…

Beilinson--Bernstein localisation relates representations of a Lie algebra $\mathfrak{g}$ to certain $\mathcal{D}$-modules on the flag variety of $\mathfrak{g}$. In [arXiv:2002.01540], examples of $\mathfrak{sl}_2$-representations which…

In this paper, we use the powerful tool Milnor bases to classify all the $3-$dimensional connected and locally symmetric Riemannian Lie Groups by solving system of polynomial equations of structure constants of each Lie algebra . Moreover,…

Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Following the paradigm of numerical algebraic geometry, an algebraic subvariety at a point…

We identify a class of left-invariant pseudo-Riemannian metrics on Lie groups for which the Laplace-Beltrami equation reduces to a first-order PDE and admits exact solutions. The defining condition is the existence of a commutative ideal…

There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting…

In this study, we classify some soliton nilpotent Lie algebras and possible candidates in dimension 8 and 9 up to isomorphy. We focus on 1 < 2 < ::: < n type of derivations where n is the dimension of the Lie algebras. We present algorithms…

We give necessary conditions for certain real analytic tube generic submanifolds in C^n to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in C^n. During…

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus…

There is a natural homomorphism of Lie pseudoalgebras from local vector fields to local rotations on a Riemannian manifold. We address the question whether this homomorphism is unique and give a positive answer in the perturbative regime…

We present structural properties of Lie algebras admitting symmetric, invariant and nondegenerate bilinear forms. We show that these properties are not satisfied by nilradicals of parabolic subalgebras of real split forms of complex simple…

We analyse a class of non-Hermitian Hamiltonians, which can be expressed bilinearly in terms of generators of a sl(2,R)-Lie algebra or their isomorphic su(1,1)-counterparts. The Hamlitonians are prototypes for solvable models of Lie…

For an arbitrary subalgebra $\mathfrak{h}\subset\mathfrak{so}(r,s)$, a polynomial pseudo-Riemannian metric of signature $(r+2,s+2)$ is constructed, the holonomy algebra of this metric contains $\mathfrak{h}$ as a subalgebra. This result…

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of…

We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional…

For every field $F$ which has a quadratic extension $E$ we show there are non-metabelian infinite-dimensional thin graded Lie algebras all of whose homogeneous components, except the second one, have dimension $2$. We construct such Lie…