相关论文: Introducing supersymmetric frieze patterns and lin…
We investigate the bounded composition operators induced by linear fractional self-maps of the right half-plane $\mathbb{C}_+$ on the Hardy space $H^2(\mathbb{C}_+).$ We completely characterize which of these operators are cohyponormal and…
The paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra…
In infinite-dimensional Hilbert spaces, the application of the concept of quasi-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to problems related to the definition of the metric operator. We discuss…
We introduce a notion of ``hereditarily antisymmetric'' operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and…
In this brief note we give a superspace description of the supersymmetric nonlocal Lorentz noninvariant actions recently proposed by Cohen and Freedman. This leads us to discover similar terms for gauge fields.
We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\"obius superalgebra $osp(1|2)$. We…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
We focus on the geometrical reformulation of free higher spin supermultiplets in $4\rm{D},~\mathcal{N}=1$ flat superspace. We find that there is a de Wit-Freedman like hierarchy of superconnections with simple gauge transformations. The…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The…
Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures and local analytic coordinates in terms of…
Applying ideas of fractional analogue of Monge-Amp\'ere operator by L. Caffarelli and F. Charro, we consider an analogue of fractional k-Hessian operators expressed as concave envelopes of fractional linear operators, and reproduce the same…
The fundamental symmetries in gravity and gauge theories, formulated using differential forms, are gauge transformations and diffeomorphisms. These symmetries act in distinct ways on different dynamical fields. Yet, the commutator of these…
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new…
In this paper we establish a hypoellipticity result for second order linear operators comprised by a linear combination, with infinite vanishing coefficients, of subelliptic operators in separate spaces. This generalizes previous known…
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…
In this paper we study in a Hilbert space a homogeneous linear second order difference equation with nonconstant and noncommuting operator coefficients. We build its exact resolutive formula consisting in the explicit non-iterative…
We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and…