Related papers: Cosymmetries and Nijenhuis recursion operators for…
In this paper, we present a new algorithm and an experimental implementation for factoring elements in the polynomial n'th Weyl algebra, the polynomial n'th shift algebra, and ZZ^n-graded polynomials in the n'th q-Weyl algebra. The most…
A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Fr\"olicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is…
We discuss the simultaneous diagonalization of a family of commuting difference operators by Koornwinder's multivariable generalization of the Askey-Wilson polynomials. The operators constitute a complete set of quantum integrals for a…
A bounded operator $T$ on a separable, complex Hilbert space is said to be odd symmetric if $I^*T^tI=T$ where $I$ is a real unitary satisfying $I^2=-1$ and $T^t$ denotes the transpose of $T$. It is proved that such an operator can always be…
In this paper, we consider deformations of Lie 2-algebras via the cohomology theory. We prove that a 1-parameter infinitesimal deformation of a Lie 2-algebra $\g$ corresponds to a 2-cocycle of $\g$ with the coefficients in the adjoint…
We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…
The aim of this paper is to provide a cohomology of $n$-Hom-Lie color algebras governing one parameter formal deformations. Then, we study formal deformations of a $n$-Hom-Lie color algebra and introduce the notion of Nijenhuis operator on…
We study $\mathcal{O}$-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of $\mathcal{O}$-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter…
The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…
The title refers to the nilcommutative or $NC$-schemes introduced by M. Kapranov in math.AG/9802041. The latter are noncommutative nilpotent thickenings of commutative schemes. We consider also the parallel theory of nil-Poisson or…
In this paper we examine an inverse problem in the modular theory of von Neumann algebras in the case of finite factors. First we give a characterization of cyclic and separating vectors for finite factors in terms of operators associated…
We construct new examples of multidimensional commuting matrix differential operators and a multidimensional analog of the Kadomtsev--Petviashvili hierarchy.
We define two $(n+1)$ graded Lie brackets on spaces of multilinear mappings. The first one is able to recognize $n$-graded associative algebras and their modules and gives immediately the correct differential for Hochschild cohomology. The…
We provide an algebraic perspective on Nielsen--Ninomiya-type no-go theorems arising from group cohomological anomalies, revisiting in particular the version proved by Kapustin and Sopenko. Departing from their analytic proof, our approach…
New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the…
We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions of families of such operators. In one direction, we show that any homogeneous conformally variational scalar…
Integrals of motion are constructed from noncommutative (NC) Kepler dynamics, generating $SO(3),$ $SO(4),$ and $SO(1,3)$ dynamical symmetry groups. The Hamiltonian vector field is derived in action-angle coordinates, and the existence of a…
Recently a new formalism for perturbations of Maxwell's equations on the background of the Kerr-NUT-(A)dS spacetime was proposed, with which the equations are reduced to a equation of motion of a scalar field that can be solved by…
We consider a compact Riemann surface $\mathscr{R}$ with a complex of non-intersecting Jordan curves, whose complement is a pair of Riemann surfaces with boundary, each of which may be possibly disconnected. We investigate conformally…
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…