Related papers: Do Killing-Yano tensors form a Lie Algebra?
A Nijenhuis mock-Lie algebra is a mock-Lie algebra equipped with a Nijenhuis operator. The purpose of this paper is to extend the well-known results about Nijenhuis mock-Lie algebras to the realm of mock-Lie bialgebras. It aims to…
The paper studies non-Lie symmetry of the Klein-Gordon-Fock equation (KGF) in $(p+q)$-dimensional Minkowsky space. Full set of symmetry operators for the $n$-order KGF equation was explicitly calculated for arbitrary $n<\infty$ and $p+q…
We present a detailed study of a parametric Lie algebra encompassing the symmetry algebras of various models, both continuous and discrete. This algebraic structure characterizes the isotropic oscillator (with positive, purely imaginary,…
Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics,…
We present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fields about a given point on the manifold. Spaces of constant…
A new structure, based on joining copies of a group by means of a \emph{twist}, has recently been considered to describe the brackets of the two exceptional real Lie algebras of type $G_2$ in a highly symmetric way. In this work we show…
Valence two Killing tensors in the Euclidean and Minkowski planes are classified under the action of the group which preserves the type of the corresponding Killing web. The classification is based on an analysis of the system of…
This paper examines the geometry of left-invariant vector fields on five-dimensional, simply connected, nilpotent Lie groups equipped with left-invariant Riemannian metrics. Using the canonical identification between the Lie algebra and the…
Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in the velocities…
This paper presents a simple method for investigating spacetime symmetry for a given metric. The method makes use of the curvature conditions that are obtained from the Killing equations. We use the solutions of the curvature conditions to…
We describe completely conformal Killing or conformal Killing-Yano (CKY) $p$-forms on almost abelian metric Lie algebras. In particular we prove that if a $n$-dimensional almost abelian metric Lie algebra admits a non-parallel CKY $p$-form,…
Conformal rescaling of conformal Yano--Killing tensors and relations between Yano and CYK tensors are discussed. Pullback of these objects to a submanifold is used to construct all solutions of a CYK equation in anti-de Sitter and de Sitter…
By using conformal Killing-Yano tensors, and their generalisations, we obtain scalar potentials for both the source-free Maxwell and massless Dirac equations. For each of these equations we construct, from conformal Killing-Yano tensors,…
In a previous article it was proved that the extensions of the Taub-NUT geometry do not admit Killing-Yano tensors, even if they possess St\" {a}ckel-Killing tensors. Here the analysis is taken further, and it is shown that, in general,…
Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors \theta with an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which…
In this paper, we prove several Liouville-type theorems on the non-existence of Killing-Yano tensors, Killing tensors, and harmonic symmetric tensors on Hadamard manifolds and, in particular, on Riemannian symmetric spaces of non-compact…
We classify kinematical Lie algebras in dimension $D \geq 4$. This is approached via the classification of deformations of the relevant static kinematical Lie algebra. We also classify the deformations of the universal central extension of…
In recent years, averaging operators on Lie algebras (also called embedding tensors in the physics literature) and associated tensor hierarchies form an efficient tool for constructing supergravity and higher gauge theories. A Lie algebra…
In the framework of the General Relativity we show that from three generalizations of Killing vector fields, namely f-symbols, symmetric St\"{a}ckel-Killing and antisymmetric Killing-Yano tensors, some conserved currents can be obtained…
In this paper, we develop a construction of Poisson $n$-Lie algebras arising from $n$-Lie algebras of Jacobians and establish conditions under which this construction yields a Poisson $n$-Lie algebra. We also formulate a general conjecture…