Related papers: Classification of twisted generalized Weyl algebra…
We consider the first Weyl algebra, A, in the Euler gradation, and completely classify graded rings B that are graded equivalent to A: that is, the categories gr-A and gr-B are equivalent. This includes some surprising examples: in…
We generalize I. Frenkel's orbital theory for non twisted affine Lie algebras to the case of twisted affine Lie algebras using a character formula for certain non-connected compact Lie groups.
We present an algebraic classification, based on the null alignment properties of the Weyl tensor, of the general Kundt class of spacetimes in arbitrary dimension for which the non-expanding, non-twisting, shear-free null direction \boldk…
For the algebraic group $SL_{l+1}(\mathbb{C})$ we describe a system of positive roots associated to conjugacy classes in its Weyl group. Using this we explicitly describe the algebra of regular functions on certain transverse slices to…
In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as a subalgebra of the ring of invariants of a certain noncommutative ring with respect to the action of $S_1\times S_2\times\cdots\times S_n$, where $S_j$ is…
We compute the isomorphism class in $\mathfrak{KK}^{alg}$ of all noncommutative generalized Weyl algebras $A=\CC[h](\sigma, P)$, where $\sigma(h)=qh+h_0$ is an automorphism of $\CC[h]$, except when $q\neq 1$ is a root of unity. In…
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…
The Basic Universal Deformation Formula is proven and applied to show that Weyl algebras, which encode Heisenberg's uncertainty principle, are effective deformations of polynomial rings, and that uncertainty is necessary for stability.…
For any Hecke symmetry $R$ there is a natural quantization $A_n(R)$ of the Weyl algebra $A_n$. The aim of this paper is to study some general ring-theoretic aspects of $A_n(R)$ and its relations to formal deformations of $A_n$. We also…
We present the algebraic classification of the gravitational field in four-dimensional general metric-affine geometries, thus extending the current results of the literature in the particular framework of Weyl-Cartan geometry by the…
Strongly $\mathbb{Z}$-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras $\mathcal{B}(p;q, 0)$ (over a ring of polynomials in one variable) are…
The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra ${\rm gr}_v(R)$ of a subring $(R,\mathfrak{m})$ of a valuation ring…
We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain…
This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…
Generalized Weyl Algebras (GWAs) appear in diverse areas of mathematics including mathematical physics, noncommutative algebra, and representation theory. We study the invariants of quantum GWAs under finite automorphisms. We extend a…
We introduce and begin to study Lie theoretical analogs of symplectic reflection algebras for a finite cyclic group, which we call "cyclic double affine Lie algebra". We focus on type A : in the finite (resp. affine, double affine) case, we…
We investigate the spinor classification of the Weyl tensor in five dimensions due to De Smet. We show that a previously overlooked reality condition reduces the number of possible types in the classification. We classify all vacuum…
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…
In this note we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order)…