Related papers: Weyl's Theory in the Generalized Lie Algebroids Fr…
We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We demonstrate the procedure of Weyl gauging on two examples in particular: General…
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their…
The theory of generalized Weyl algebras is used to study the $2\times 2$ reflection equation algebra $\mathcal{A}=\mathcal{A}_q(\operatorname{M}_2)$ in the case that $q$ is not a root of unity, where the $R$-matrix used to define…
We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…
This article shows that the approach to generalised curvature and torsion pioneered by Polacek and Siegel [1] is a generalisation of Cartan Geometry -- rendering latter natural from the point of view of O(d,d)-generalised geometry. We…
We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in an Integrable Weyl-Dirac theory proposed in Found. Phys. 29, 1303 (1999). The main differences between these solutions and the…
Recently, a birational representation of an extended affine Weyl group of $(A_{2N}\rtimes A_1)^{(1)}$-type, which gives a higher-order generalization of an $A_4^{(1)}$-surface type $q$-Painlev\'e equation, was obtained. In this paper, we…
Motivated by work of Kac and Lusztig, we define a root system and a Weyl groupoid for a large class of semisimple Yetter-Drinfeld modules over an arbitrary Hopf algebra. The obtained combinatorial structure fits perfectly into an existing…
We propose a new approach to superrigidity phenomena and implement it for lattice representations and measurable cocycles with homeomorphisms of the circle as the target group. We are motivated by Ghys' theorem stating that any…
Here is discussed generalization of Clifford algebras, l^n-dimensional Weyl-Clifford algebras T(n,l) with n generators t_k satisfying equation $(\sum_{k=1}^n a_k t_k)^l = \sum_{k=1}^n a_k^l$. It is originated from two basic and well known…
Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and "geometrize" electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the…
We generalize the electrical Lie algebras originally introduced by Lam and Pylyavskyy in several ways. To each Kac-Moody Lie algebra $\mathfrak{g}$ we associate two types (vertex type and edge type) of the generalized electrical algebras.…
We define Weil spaces, Weil manifolds, Weil varieties and Weil Lie groups over an arbitrary commutative base ring K (in particular, over discrete rings such as the integers), and we develop the basic theory of such spaces, leading up the…
We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from…
A scale invariant theory of gravity, containing at most two derivatives, requires, in addition to the Riemannian metric, a scalar field and (or) a gauge field. The gauge field is usualy used to construct the affine connection of Weyl…
The Weil correspondence states that the datum of a Seiberg-Witten differential is equivalent to an algebraic group extension of the integrable system associated to the Seiberg-Witten geometry. Remarkably this group extension represents…
In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor)…
Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…