Related papers: Simple Witt modules that are finitely generated ov…
The Lie superalgebra $W(\infty)$ is defined to be the direct limit of the simple finite-dimensional Cartan type Lie superalgebras $W(n)$ as $n$ goes to infinity, where $W(n)$ denotes the Lie superalgebra of superderivations of the Grassmann…
We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.
We determine the characters of the simple composition factors and the submodule lattices of certain Weyl modules for classical groups. The results have several applications. The simple modules arise in the study of incidence systems in…
We construct all finite irreducible modules over Lie conformal superalgebras of type K
Let $n\geq 2$ be an integer, $S_n$ be the Lie algebra of vector fields on $\mathbb{C}^n$ with zero divergence, and $D_n$ be the Weyl algebra over the polynomial algebra $A_n=\mathbb{C}[t_1,t_2,\cdots,t_n]$. In this paper, we study the…
Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…
We study the constructible Witt theory of \'etale sheaves of $\Lambda$-modules on a scheme $X$ for coefficient rings $\Lambda$ having finite characteristic not equal to 2 and prime to the residue characteristics of the scheme $X$. Our…
We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with…
Over a field $F$ of any characteristic, for a commutative associative algebra $A$ with an identity element and for the polynomial algebra $F[D]$ of a commutative derivation subalgebra $D$ of $A$, the associative and the Lie algebras of Weyl…
In this paper, we study weight representations over the Schr{\"o}dinger Lie algebra $\mathfrak{s}_n$ for any positive integer $n$. It turns out that the algebra $\mathfrak{s}_n$ can be realized by polynomial differential operators. Using…
The aim of this paper is to give relations between the category of finetely generated graded modules over the homogeneized Weyl algebra $B_{n}$, the finetely generated modules over the Weyl algebra $A_{n}$ and the finetely generated graded…
This article undertakes an exploration of simple modules of 3-cyclic quantum Weyl algebra at roots of unity. Under the roots of unity assumption, the algebra becomes a Polynomial Identity algebra and the vector space dimension of the simple…
Let X be the group of weights of a maximal torus of a simply connected semisimple group over C and let W be the Weyl group. The semidirect product W(Q\otimes X/X) is called the extended Weyl group. There is a natural C(v)-algebra H called…
The Witt algebra W_n is the Lie algebra of all derivations of the n-variable polynomial ring V_n=C[x_1, ..., x_n] (or of algebraic vector fields on A^n). A representation of W_n is polynomial if it arises as a subquotient of a sum of tensor…
Let $K$ be an algebraically closed field of characteristic zero, $A= K[x_1, \dots, x_n]$ the polynomial ring in $n$ variables, and let $W_n(K)$ be the Lie algebra of all $K$-derivations of $A.$ This Lie algebra also is the free $A$-module…
In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of…
We establish the existence of the Bernstein polynomial in one indeterminate $t$, and provide a method for its explicit computation. The Bernstein polynomial is associated with finitely generated modules over the Weyl algebra, known as…
We describe the Witt invariants of a Weyl group over a field $k_0$ by giving generators for the $W(k_0)$-module of Witt invariants, under the assumption that the characteristic of $k_0$ does not divide the order of the group. For the Weyl…
A finitely generated module over the ring L=Z[t, t^{-1}] of integer Laurent polynomials that has no Z-torsion is determined by a pair of sub-lattices of L^d. Their indices are the absolute values of the leading and trailing coefficients of…
The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension \hat{SD}. For each c\in C, the vacuum module M_c(\hat{SD}) of central charge c admits a vertex superalgebra structure, and…