Related papers: Simple modules of small quantum groups at dihedral…

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

For a simple Lie algebra L of type A, D, E we show that any Belavin-Drinfeld triple on the Dynkin diagram of L produces a collection of Drinfeld twists for Lusztig's small quantum group u_q(L). These twists give rise to new…

Let $k$ be an algebraically closed field of odd characteristic $p$, and let $D_n$ be the dihedral group of order $2n$ such that $p\mid 2n$. Let $D(kD_n)$ denote the quantum double of the group algebra $kD_n$. In this paper, we describe the…

We classify the simple infinite dimensional integrable modules with finite dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

In this paper, we study irreducible weight modules with infinite dimensional weight spaces over the mirror-twisted Heisenberg-Virasoro algebra $\mathcal{D}$. More precisely, the necessary and sufficient conditions for the tensor products of…

We generalise the quantum double construction of Drinfel'd to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the *-algebra structure of the quantum double. If the conjugacy…

Let $q$ be an $n^{th}$ root of unity for $n > 2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-J\"urgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an…

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…

Using simple modules over the derivation Lie algebra $C[t]\frac{d}{d t}$ of the associative polynomial algebra $C[t]$, we construct new weight Virasoro modules with all weight spaces infinite dimensional. We determine necessary and…

The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for $E_{8}$ or its highest weight is minuscule. In this paper, we prove…

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

Consider a field k of characteristic p > 0, G_r the r-th Frobenius kernel of a smooth algebraic group G, DG_r the Drinfeld double of G_r, and M a finite dimensional DG_r-module. We prove that the cohomology algebra H*(DG_r,k) is finitely…

We extend the Larson-Sweedler theorem to weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We show that the category of modules over a weak Hopf…

Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to…

It is shown that Nichols algebras over alternating groups A_m, m>4, are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to A_m is isomorphic to the group…

We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from…

The conformal Galilei algebra (CGA) is a non-semisimple Lie algebra labelled by two parameters $d$ and $\ell$. The aim of the present work is to investigate the lowest weight representations of CGA with $d = 1$ for any integer value of…

In this paper, Whittaker modules are studied for a subalgebra $\mathfrak{q}_{\epsilon}$ of the $\emph{N}$=2 superconformal algebra. The Whittaker modules are classified by central characters. Additionally, criteria for the irreducibility of…

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…