33 Results Found

In this paper, we mainly study free $U\left(\mathfrak{h}\right)$-modules over the $N=1$ Heisenberg–Virasoro superalgebra. We construct a family of non-weight modules that are free of rank 2 when regarded as modules over the Cartan subalgebra. Moreover, we classify the f...

We show that given a Lie superalgebra and an element of its dual space, one can construct the 3-Lie superalgebra. We apply this approach to Lie superalgebra of $(m,n)$ -block matrices taking a supertrace of a matrix as the element of dual sp...

Over a field of characteristic $p>3$, let $KO(n,n+1;\underline{t})$ denote the odd contact Lie superalgebra. In this paper, the super-biderivations of odd Contact Lie superalgebra $KO(n,n+1;\underline{t})$ are studied. Let $T_{KO}$ be a torus of $KO(n,n+1;\underline{t})$, which...

We construct a finite-dimensional Z₃-graded Lie superalgebra of dimensions (12,4,3), featuring a grade-2 sector that obeys a cubic bracket relation with the fermionic sector. This induces an emergent triality symmetry cycling the three components. Th...

Let R be a 2-torsion-free and $n!$-torsion-free commutative ring with unity, and let X be a locally finite preordered set. We endow the incidence algebra $I(X,R)$ with a superalgebra structure via a nontrivial idempotent, which decomposes $I(X,R)$ into eve...

The main goal of this paper was to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, and ${\alpha }^k$-derivations and provide a classification in low dimension. We introduce a...

This work presents a graded investigation of $\mathrm{\Theta }$-superderivations within the framework of Lie superalgebras, generalizing the $\mathrm{\Theta }$-derivation concept from ordinary Lie algebras to graded settings. For a given Lie superalgebra $\mathfrak{g}$, a linear mappi...

Let $n\ge 2$ be a fixed integer. The aim of this paper is to investigate the properties of n-derivations within the framework of perfect Lie superalgebras over a commutative ring R. The main result shows that if the base ring contains ${\displaystyle \frac{1}{n-1}}$, and L...

This paper investigates functional identities in superalgebras, building on Wang’s foundational work. We study d-superfree subsets and k-supercommuting maps in prime superalgebras, both with and without superinvolution, introducing new results...

We study generalized derivations of complex multiplicative ${\alpha }^2$-weighted $\Omega$-Hom-Lie superalgebras. The chosen structural identity is shown to be stable under Yau twisting, and every regular algebra in this class untwists canonically to an $\&O$...

In this paper we compute the Betti numbers for complex nilpotent Lie superalgebras of dimension $\le 5$ .

This paper performed an investigation into the s-embedding of the Lie superalgebra $\overrightarrow{(}{S}^{1\mid 1})$, a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-...

This paper introduces the notions of BiHom-superdialgebras and BiHom-Leibniz superalgebras, which generalize Hom-superdialgebras and BiHom-dialgebras to the super setting with two commuting homomorphisms. We establish the fundamental properties of th...

Let $n\ge 2$ be fixed, and let $\Lambda$ be a Lie superalgebra over a commutative ring R. We investigate the structure of the algebra ${\mathrm{Der}}_n(\Lambda )$ of n-derivations. We show that ${\mathrm{Der}}_n(\Lambda )$ is a ${\mathbb{Z}}_2$-graded Lie superalgebra and that its elements pres...

In this paper we study superderivations and Jordan superderivations of incidence superalgebras of locally finite ${\mathbb{Z}}_2$-graded posets. We prove that every superderivation can be expressed as a sum of an inner superderivation, an additive superderivation,...

We successively reanalyzed modern Lie-algebraic approaches lying in the background of effective constructions of integrable super-Hamiltonian systems on functional $N=1,2,3$- supermanifolds, possessing rich supersymmetries and endowed with suitably rel...

We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using...

We construct certain modified highest weight modules which are called quasi highest weight modules in this paper. Using the quasi highest weight modules, we introduce a new category of modules over an affine Lie superalgebra which contains projective...

In this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivale...

Lie-algebraic Poisson structures, related to the superalgebra of super-pseudodifferential operators on the circle over the even component of the ${\mathbb{Z}}_2$-graded Grassmann algebra, have been studied in detail; the corresponding coadjoint orbits, generated b...

We survey the recent developments on quantum invariants of 3-manifolds and links: $\widehat{Z}$ and $F_L$. They are q-series invariants originated from mathematical physics, inspired by the categorification of a numerical quantum invariant—the Witten–R...

A new formalism involving spinors in theories of spacetime and vacuum is presented. It is based on a superalgebraic formulation of the theory of algebraic spinors. New algebraic structures playing role of Dirac matrices are constructed on the basis o...

We study an interesting superization problem of integrable nonlinear dynamical systems on functional manifolds. As an example, we considered a quantum many-particle Schrödinger–Davydov model on the axis, whose quasi-classical reduction pro...

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra ${\mathfrak{g}}_{\mathsf{u}}$ that extends ${\mathbf{e}}_{\mathbf{9}}$. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn ${\mathfrak{g}}_{\mathsf{u}}$ into a Lie superalgebra ${\mathfrak{sg}}_{\mathsf{u}}$ with no super...

In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is...

We studied the Gaudin models with $\mathfrak{gl}\left(1\right|1)$ symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation $\mathfrak{gl}\left(1\right|1\left)\right[t]$-modules. Namely, we gave an explicit description of the algebra of Hamiltonians (Gaudin Hamilt...

A research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings and braided group st...

An exciting subject in string theory is to consider some applications of the AdS/CFT correspondence to realistic systems like condensed matter systems. Since most of such systems are non-relativistic, an anisotropic scaling symmetry with the general...

In supersymmetric extensions of the Standard Model, the observed particles come in fermion–boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles, not a sing...

This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various comp...

Warm dark matter particles with masses in the keV range have been linked with the large group representations in gauge theories through a high number of species at decoupling. In this paper, we address WDM fermionic degrees of freedom from such repre...

The Landau problem and harmonic oscillator in the plane share a Hilbert space that carries the structure of Dirac’s remarkable $so(2,3)$ representation. We show that the orthosymplectic algebra $osp\left(1\right|4)$ is the spectrum generating algebra for the...

We reformulate holographic space–time models in terms of Hilbert bundles over the space of the time-like geodesics in a Lorentzian manifold. This reformulation resolves the issue of the action of non-compact isometry groups on finite-dimensiona...