Related papers: Generalized supersymmetry and L\'evy-Leblond equat…
A Lie superalgebra is called quasi-Frobenius if it admits a closed anti-symmetric non-degenerate bilinear form. We study the notion of double extensions of quasi-Frobenius Lie superalgebra when the form is either orthosymplectic or…
We describe the solutions to a family of rotationally symmetric second order partial differential equations in the complex plane that arises from a four-dimensional complex Lie algebra whose spanning set generates the algebra from which…
We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This…
We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…
So far, there are described in the literature two ways to superize the Liouville equation: for a scalar field (for $N\leq 4$) and for a vector-valued field (analogs of the Leznov--Saveliev equations) for N=1. Both superizations are…
A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges.…
By solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy. As an application, we establish…
An N=4 supersymmetric extension of the l-conformal Galilei algebra is constructed. This is achieved by combining generators of spatial symmetries from the l-conformal Galilei algebra and those underlying the most general superconformal…
The Amitsur-Levitzki identity for matrices was generalized in several directions: by Kostant for simple finite-dimensional Lie algebras, by Kirillov (later joined by Kontsevich, Molev, Ovsienko, and Udalova) for simple vectorial Lie…
In the Wess-Zumino gauge, supersymmetry transformations become non-linear and are usually incorporated together with BRS transformations in the form of Slavnov-Taylor identities, such that they appear at first sight to be even non-local.…
A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized…
Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, \textit{i.e.}, classes of differential equations that are in correspondence with their Lie point symmetries. In particular,…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
The supermembrane in light-cone gauge gives rise to a supersymmetric quantum mechanics system with SU(N) gauge symmetry when the group of area preserving diffeomorphisms is suitably regulated. de Wit, Marquard and Nicolai showed how…
Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the $\mathcal{N}=1$ Super-Yang-Mills (SYM) theory with gauge…
By using the Lie's invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schr\"{o}dinger equations with variable coefficients. Starting from the equivalence generators we construct…
Lagrangian gauge theories with a z=2 Lifshitz scaling provide a family of interacting, asymptotically free five-dimensional field theories. We examine some of their quantum properties, extending previous results to include matter. We…
Consider a Leibniz superalgebra $\mathfrak L$ additionally graded by an arbitrary set $I$ (set grading). We show that $\mathfrak L$ decomposes as the sum of well-described graded ideals plus (maybe) a suitable linear subspace. In the case…
Using advantages of nonstandard computational techniques based on the light-cone variables, we explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein-Gordon equation. This allows us to describe this algebra in…
The equations of open 2-dimensional Toda lattice (TL) correspond to Leznov-Saveliev equations (LSE) interpreted as zero-curvature Yang-Mills equations on the variety of $O(3)$-orbits on the Minkowski space when the gauge algebra is the…