Related papers: Blocks of Lie Superalgebras of Type W(n)

We consider the category of Whittaker modules for the Lie superalgebra $W_{m,n}$ of vector fields on $\mathbb{C}^{(m|n)}$. For any $\mathbf{a}\in \mathbb{C}^m$ we show the equivalence between the blocks $\Omega_{\mathbf…

Simple modules for the restricted Witt superalgebra $W(m,n,1)$ are considered. Conditions are provided for the restricted and nonrestricted Kac modules to be simple.

Let $\mathfrak{W}$ be the Lie algebra of vector fields on the line. Via computing extensions between all simple modules in the category $\mathcal{O}$, we give the block decomposition of $\mathcal{O}$, and show that the representation type…

In the present paper we classify all irreducible continuous representations of the simple linearly compact n-Lie superalgebra of type W. The classification is based on a bijective correspondence between the continuous representations of the…

For the two Cartan type S subalgebras of the Witt algebra $\W_n$, called Lie algebras of divergence-zero vector fields, we determine all module structures on the universal enveloping algebra of their Cartan subalgebra $\h_n$. We also give…

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we study other possible matrix formats and in particular the so-called diagonal format which…

We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…

Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra…

Let $n>1$ be an integer. The algebras of the title, which we abbreviate as algebras of type $n$, are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, which are generated by an element of degree $1$ and an element…

In this paper, we introduce two new families of infinite-dimensional simple Lie algebras and a new family of infinite-dimensional simple Lie superalgebras. These algebras can be viewed as generalizations of the Block algebras.

Let $L$ be a Lie superalgebra over a field of characteristic different from $2,3$ and write $\mathrm{ID}^{*}(L)$ for the Lie superalgebra consisting of superderivations mapping $L$ to $L^{2}$ and the central elements to zero. In this paper…

Let $\mathbb F$ be a field $\mathbb F $ of characteristic zero. Let $W_{n}(\mathbb F)$ be the Lie algebra of all $\mathbb F$-derivations with the Lie bracket $[D_1, D_2]:=D_1D_2-D_2D_1$ on the polynomial ring $\mathbb F [x_1, \ldots ,…

Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in…

Let $\mathbb{k}$ be an algebraically closed field of characteristic $ p>0. $ In this short note, we illustrate a class of Lie superalgebras over $ \mathbb{k} $ such that the category of restricted supermodules is of one block. As an…

We classify the quasifinite highest weight modules over a family of subalgebras W_{\infty}^{n} of the central extension W_{1+\infty} of the Lie algebra of differential operators on the circle consisting of operators of order \geq n. We…

A loop-algebraic presentation is given for toroidal Lie superalgebras of classical types. Based on the loop superalgebra presentation free field realizations of toroidal Lie superalgebras are constructed for types $A(m,n)$, $B(m,n)$, C(n)…

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…

We consider the finite Weyl groups of classical type -- $W(A_{r})$ for $r \geq 1$, $W(B_{r}) = W(C_{r})$ for $r \geq 2$, and $W(D_{r})$ for $r \geq 4$ -- as supergroups in which the reflections are of odd superdegree. Viewing the…

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…