Related papers: Generalized permutation matrices and non-weight mo…

We study the indecomposable summands of the permutation module obtained by inducing the trivial $\mathbb{F}(S_a\wr S_n)$-module to the full symmetric group $S_{an}$ for any field $\mathbb{F}$ of odd prime characteristic $p$ such that…

With the aid of the exponentiation functor and Fourier transform we introduce a class of modules $T(g,V,S)$ of $\mathfrak{sl} (n+1)$ of mixed tensor type. By varying the polynomial $g$, the $\mathfrak{gl}(n)$-module $V$, and the set $S$, we…

In the present paper, a class of non-weight modules over the super-BMS$_3$ algebras $\S^{\epsilon}$ ($\epsilon=0$ or $\frac{1}{2}$) are constructed. Assume that $\mathfrak{t}=\C L_0\oplus\C W_0\oplus\C G_0$ and $\mathfrak{T}=\C L_0\oplus\C…

The classification problem for simple $\mathfrak{sl}(2)$-modules leads in a natural way to the study of the category of finite rank torsion free $\mathfrak{sl}(2)$-modules and its subcategory of rational $\mathfrak{sl}(2)$-modules. We prove…

The generalized quantum group $\mathcal{U}(\epsilon)$ of type $A$ is an affine analogue of quantum group associated to a general linear Lie superalgebra $\mathfrak{gl}_{M|N}$. We prove that there exists a unique $R$ matrix on tensor product…

We study the problem of indecomposability of translations of simple modules in the principal block of BGG category $\mathcal{O}$ for $\mathfrak{sl}_n$, as conjectured in \cite{KiM}. We describe some general techniques and prove a few…

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…

In this paper, we study the category of modules over the Smith algebra which are free of finite rank over the unital polynomial subalgebra generated by the Cartan element $h$ and obtain families of such simple modules of arbitrary rank. In…

In this paper, we give a complete classification of all free $U(\mathbb{C}L_0 \oplus \mathbb{C}Y_0\oplus \mathbb{C}M_0)$-modules of rank 1 over a Schr{\"o}dinger-Virasoro type algebra $\mathfrak{tsv}$.

Rank $1$ modules are the building blocks of the category ${\rm CM}(B_{k,n}) $ of Cohen-Macaulay modules over a quotient $B_{k,n}$ of a preprojective algebra of affine type $A$. Jensen, King and Su showed in \cite{JKS16} that the category…

We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…

It is known that the category $\mathscr{C}^H$ of nilpotent weight modules over the quantum group associated with the super Lie algebra $\mathfrak{sl}(2|1)$ is a relative pre-modular $G$-category. Its modified trace enables to define an…

Let $H_{\mathbf{k}}$ be a symplectic reflection algebra corresponding to a cyclic subgroup $\Gamma \subseteq SL_2 \C$ of order $n$ and $U_{\mathbf{k}} = eH_{\mathbf{k}} e$ the spherical subalgebra of $H_{\mathbf{k}}$. We show that for…

We give a classification of infinite dimensional indecomposable weight modules over the Lie superalgebra $sl(2/1)$.

If $\mathfrak{g} = \mathfrak{g}_{\overline{0}} \oplus \mathfrak{g}_{\overline{1}}$ is a Lie superalgebra over an algebraically closed field $k$ of characteristic 0, the notion of an endotrivial module has recently been extended to…

We study the structure of the space of covariants $B:=\left(\bigwedge (\mathfrak g/\mathfrak k)^*\otimes \mathfrak g\right)^{\mathfrak k},$ for a certain class of infinitesimal symmetric spaces $(\mathfrak g,\mathfrak k)$ such that the…

Let $\mathfrak F$ be a formation and let $G$ be a group. A subgroup $H$ of $G$ is $\mathrm{K}\mathfrak F$-subnormal (submodular) in $G$ if there is a subgroup chain $H=H_0\le \ H_1 \le \ \ldots \le H_i \leq H_{i+1}\le \ldots \le \ H_n=G$…

We study modules over a generalized Weyl algebra $R(\sigma,a)$ which are free when restricted to the base ring $R$. When $R$ is an integral domain, we construct all such finite-rank modules up to isomorphism, leading to new simple modules…

We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…

Motivated by Kraji\v{c}ek and Scanlon's definition of the Grothendieck ring $K_0(M)$ of a first-order structure $M$, we introduce the definition of $K$-groups $K_n(M)$ for $n\geq0$ via Quillen's $S^{-1}S$ construction. We provide a recipe…