Related papers: On a category of $gl_{\infty}$-modules

In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $\mathbb{Z}^+$-graded Lie conformal algebras…

We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…

We describe the category of integrable sl(1|n)^ -modules with the positive central charge and show that the irreducible modules provide the full set of irreducible representations for the corresponding simple vertex algebra.

We study the structure of tensor products of $\mathfrak{gl}(\infty) = \varinjlim \mathfrak{gl}(n)$-modules $\mathbf L(\mathbf \lambda) \otimes \mathbf F$ where $\mathbf L(\mathbf \lambda)$ is a simple integrable highest weight module and…

Let $G$ be an arbitrary additive subgroup of $C$ and $Vir[G]$ the corresponding generalized Virasoro algebra. In the present paper, irreducible weight modules with finite dimensional weight spaces over $Vir[G]$ are completely determined.…

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of a finite number of irreducible modules $M(\lambda, \alpha, \beta, \gamma)$ with irreducible highest weight…

We study the finite dimensional modules on the half-quantum group u_q^+ at a root of unity q, whose action can be extended to u_q (quotient of the quantized enveloping algebra of sl_2). We derive decomposition formulas of the tensor product…

We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of submodules at all. More generally, we show that a natural…

Let $k$ be an algebraically closed field of characteristic $p>0$. In this master thesis, we classify multiplicity-free tensor products of simple modules for the groups $SL_2(k)$ and $SL_3(k)$. We also provide a classification for $SL_n(k)$…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

In this paper we study categories of tilting modules. Our starting point is the tilting modules for a reductive algebraic group G in positive characteristic. Here we extend the main result in [8] by proving that these tilting modules form a…

In this paper, we obtain a class of irreducible Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega(\lambda,b)$ defined in [LZ], with irreducible highest weight modules $V(\theta,h)$ or with irreducible…

We give an explicit formula for the decomposition of the tensor product of any two indecomposable non-projective modules for the symmetric group algebra $F \mathfrak{S}_p$ modulo projective modules. In particular, we show that the tensor…

Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…

We introduce and study the category of twisted modules over a triangular differential graded bocs. We show that in this category idempotents split, that it admits a natural structure of a Frobenius category, that a twisted module is…

We construct two non-semisimple braided ribbon tensor categories of modules for each singlet vertex operator algebra $\mathcal{M}(p)$, $p\geq 2$. The first category consists of all finite-length $\mathcal{M}(p)$-modules with atypical…

We contribute to the classification of modular categories $\mathcal{C}$ with $\operatorname{FPdim}(\mathcal{C})\equiv 2 \pmod 4$. We prove that such categories have group of invertibles of even order, and that they factorize as $\mathcal…

We classify completely prime primitive ideals whose associated varieties are the closure of the minimal nilpotent orbit of $\mathfrak{g}=\mathfrak{sl}(n,\mathbb{C})$, and classify irreducible $(\mathfrak{g},\mathfrak{k})$-modules which have…

The framework of templicial objects was put forth in arXiv:2302.02484v1 in order to develop higher categorical concepts in the presence of enrichment. In particular, quasi-categories in modules constitute a subclass of templicial modules…

We call a monoidal category ${\mathcal C}$ a Serre category if for any $C$, $D \in {\mathcal C}$ such that $C\ot D$ is semisimple, $C$ and $D$ are semisimple objects in ${\mathcal C}$. Let $H$ be an involutory Hopf algebra, $M$, $N$ two…