Related papers: N-commutators on vector fields

Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…

We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.

Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.

We give an off-shell formulation of the N=2 supersymmetric new nonlinear vector-tensor multiplet. Interactions arise in this model as a consequence of gauging the central charge of the supersymmetry algebra, which in contrast to previous…

The n-th order covariant derivative on a smooth manifold with an affine connection is a differential operator which turns a function into a tensor field of type (0,n). In this paper the properties of this operatior related to the…

Differential $p$-forms and $q$-vector fields with constant coefficients are studied. Differential $p$-forms of degrees $p=1,2,n-1,n$ with constant coefficients on a smooth $n$-dimensional manifold $M$ are characterized. In the contravariant…

We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.

We introduce a sl_2-invariant family of nonlinear vector fields with a non-semisimple triple zero singularity. In this paper we are concerned with characterization and normal form classification of these vector fields. We show that the…

Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I_i, i=0,...,m, be two-sided ideals of A, \GL_n(A,I_i) the principal congruence subgroup of level I_i in GL_n(A) and E_n(A,I_i) be the…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

We construct the general four-dimensional N=2 supergravity theory coupled to vector and vector-tensor multiplets only. Consistency of the construction requires the introduction of the vector fields dual to those sitting in the same…

Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…

We prove that a $IR n+1$-valued vector field on IR n is the sum of the traces of two harmonic gradients, one in each component of $IR n+1 \ IR n$ , and of a $IR n$-valued divergence free vector field. We apply this to the description of…

We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…

The notion of Gelfand pair (G, K) can be generalized if we consider homogeneous vector bundles over G/K instead of the homogeneous space G/K and matrix-valued functions instead of scalar-valued functions. This gives the definition of…

In this paper, we characterize arbitrary polynomial vector fields on $S^n$. We establish a necessary and sufficient condition for a degree one vector field on the odd-dimensional sphere $S^{2n-1}$ to be Hamiltonian. Additionally, we…

An abelian 4D, $\mathcal{N}$ = 4 vector supermultiplet allows for a duality transformation to be applied to one of its spin-0 states. The resulting theory can be described as an abelian 4D, $\mathcal{N}$ = 4 vector-tensor supermultiplet. It…

We classify degeneration patterns of Verma modules over the N=2 superconformal algebra in two dimensions. Explicit formulae are given for singular vectors that generate maximal submodules in each of the degenerate cases. The mappings…

We establish that any even permutation from A_n moving at least [3n/4] + o(n) points is the commutator of a generating pair of A_n and a generating pair of S_n. From this we deduce an exponential lower bound on the number of systems of…