Related papers: Classification of twisted generalized Weyl algebra…

Homological smoothness and twisted Calabi-Yau property of generalized Weyl algebras over polynomial algebras in two variables is studied. A necessary and sufficient condition to be homologically smooth is given. The Nakayama automorphisms…

The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogize the Schur functions. For this generalization, the…

Using $n$ finite order automorphisms on a simple complex Lie algebra we construct twisted $n$-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case $n=2$ we list certain simple Lie algebras and…

We prove that the condition \begin{equation} \sum_{n=1}^\infty\frac{1}{nw(n)}<\infty \end{equation} is necessary for an increasing sequence of numbers $w(n)$ to be an almost everywhere unconditional convergence Weyl multiplier for the…

In this paper, we associate the TKK algebra $\widehat{\mathcal{G}}(\mathcal{J})$ with vertex algebras through twisted modules. Firstly, we prove that for any complex number $\ell$, the category of restricted…

We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms…

We compute Hochschild homology and cohomology of a class of generalized Weyl algebras (for short GWA, defined by Bavula in St.Petersbourg Math. Journal 1999 4(1) pp. 71-90). Examples of such algebras are the n-th Weyl algebras, U(sl_2),…

Let $\mathtt{k}$ be an algebraically closed field of characteristic zero. Let ${\stackrel{{\rm o}}{{\mathfrak{g}}}}$ be the Lie superalgebra ${\mathfrak{sl}}(n|m)$ and let $\mathfrak{W}$ be the Weyl groupoid introduced by Sergeev and…

We associate to a semisimple complex Lie algebra $\mathfrak{g}$ a sequence of polynomials $P_{\ell,\mathfrak{g}}(x)\in\mathbb{Q}[x]$ in $r$ variables, where $r$ is the rank of $\mathfrak{g}$ and $\ell=0,1,2,\ldots $. The polynomials…

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…

We consider the problem of classifying (possibly noncommutative) R-algebras of low rank over an arbitrary base ring R. We first classify algebras by their degree, and we relate the class of algebras of degree 2 to algebras with a standard…

Let (g,[p]) be a finite-dimensional restricted Lie algebra, defined over an algebraically closed field k of characteristic p>0. The scheme of tori of maximal dimension of g gives rise to a finite group S(g) that coincides with the Weyl…

We introduce a notion of a (V,T)-module over a vertex algebra V for an arbitrary positive integer T, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A^{T}_{m}(V) for…

Global and local Weyl modules for the untwisted multiloop Lie algebras were defined by Chari, the first and the second author via homological properties. In this paper we extended the ideas to give a categorical definition of the Weyl…

In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with coexisting quadratic and cubic constitutive relations. We…

We prove that the Weyl algebra over $\mathbb{C}$ cannot be a fixed ring of any domain under a nontrivial action of a finite group by algebra automorphisms, thus settling a 30-year old problem. In fact, we prove the following much more…

Given a finite-dimensional Lie algebra, and a representation by derivations on the completed symmetric algebra of its dual, a number of interesting twisted constructions appear: certain twisted Weyl algebras, deformed Leibniz rules,…

Crystalline graded rings are generalizations of certain classes of rings like generalized twisted group rings, generalized Weyl algebras, and generalized skew crossed products. When the base ring is a commutative Dedekind domain, two…

Previously we showed that the tensor product of a weight module over a generalized Weyl algebra (GWA) with a weight module over another GWA is a weight module over a third GWA. In this paper we compute tensor products of simple and…

The Weyl and Ricci tensors can be algebraically classified in a Lorentzian spacetime of arbitrary dimensions using alignment theory. Used in tandem with the boost weight decomposition and curvature operators, the algebraic classification of…