Related papers: Weyl structures for path geometries

The group of automorphisms of the first Weyl algebra acts on commuting ordinary differential operators with polynomial coefficient. In this paper we prove that for fixed generic spectral curve of genus two the set of orbits is infinite.

We classify the band degeneracies in 3D crystals with screw symmetry $n_m$ and broken $\mathcal P*\mathcal T$ symmetry, where $\mathcal P$ stands for spatial inversion and $\mathcal T$ for time reversal. The generic degeneracies along…

We introduce a Fefferman-type construction that associates an almost Grassmannian structure of type $(2,n+1)$ to every $(n+1)$-dimensional path geometry. We prove that the construction is normal and provide two equivalent characterizing…

Let $V$ be a symplectic space over $\mathbb{C}$, $dim_\mathbb{C} V=2l$, and let $G$ be a finite subgroup of $Sp(V)$. The invariant regular functions $\mathbb{C}[V]^G$ inherit a Poisson algebra structure and so the quotient variety ${\cal…

We study geometric structures of $\mathcal{W}_4$-type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion…

In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple linear…

Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry…

We show that a fundamental sandwich algebra has an analogue of a root system of a semisimple Lie algebra. This leads to an analogue of a Weyl group, which we study in another paper.

We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…

We classify all non-abelian groups G such that there exists a pair (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional under two assumptions: the square…

We introduce the first hom-associative Weyl algebras over a field of prime characteristic as a generalization of the first associative Weyl algebra in prime characteristic. First, we study properties of hom-associative algebras constructed…

Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and…

Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are…

For any two root subsets associated with two Carter diagrams that have the same $ADE$ type and the same size, we construct the transition matrix that maps one subset to the other. The transition between these two subsets is carried out in…

The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the…

We study Hamilton circuits of the Cayley graphs of the Weyl groupoids of the generalized quantum groups, or the quantum double of the Nichols algebras of diagonal-type, with finite root systems. We prove the existence of a Hamilton circuit…

In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five…

We consider the Riemann-Hilbert factorization approach to the construction of Weyl metrics in four space-time dimensions. We present, for the first time, a rigorous proof of the remarkable fact that the canonical Wiener-Hopf factorization…

We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on…

In "Meromorphic Functions and Analytic Curves", H. and F. J. Weyl identified an intriguing connection between holomorphic curves and their associated curves, which they referred to as the "peculiar relation". In this paper, we present a…