Related papers: A construction of lower-bounded generalized twiste…

For any truncated path algebra $\Lambda$, we give a structural description of the modules in the categories ${\cal P}^{<\infty}(\Lambda\text{-mod})$ and ${\cal P}^{<\infty}(\Lambda\text{-Mod})$, consisting of the finitely generated (resp.…

This paper constructs the cohomology theory for grading-restricted vertex superalgebras, generalizing Yi-Zhi Huang's cohomology theory of grading-restricted vertex algebras. To simplify the discussion, motivate the construction, and make it…

Let $\tilde{G}$ be a finite group, $G$ a normal subgroup of $\tilde{G}$ and $k$ an algebraically closed field of characteristic $p>0$. The first main result in this paper is to show that support $\tau$-tilting $k\tilde{G}$-modules…

We construct and study the moduli of hypersurfaces in toric orbifolds. Let $X$ be a projective toric orbifold and $\alpha \in Cl(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|\alpha|$ by $G =…

In the setting of a variety $X$ admitting a tilting bundle $T$ we consider the problem of constructing $X$ as a quiver GIT quotient of the endomorphism algebra $A=\textrm{End}_X(T)^{\textrm{op}}$ corresponding to the tilting bundle. We…

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

Let $A$ and $B$ be rings, $U$ a $(B,A)$-bimodule and $T=\begin{pmatrix} A&0\\U&B \end{pmatrix}$ the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated. We…

Let $\Lg$ be a simple complex Lie algebra, we denote by $\Lhg$ the corresponding affine Kac--Moody algebra. Let $\Lambda_0$ be the additional fundamental weight of $\Lhg$. For a dominant integral $\Lg$--coweight $\lam^\vee$, the Demazure…

We give a construction of Gorenstein projective $\tau$-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $\tau$-tilting…

We introduce a Poisson version of the graded twist of a graded associative algebra and prove that every graded Poisson structure on a connected graded polynomial ring $A:=\Bbbk[x_1,\ldots,x_n]$ is a graded twist of a unimodular Poisson…

We introduce a general version of singular compactness theorem which makes it possible to show that being a $\Sigma$-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed…

In quantum groups coproducts of Lie-algebras are twisted in terms of generators of the corresponding universal enveloping algebra. If representations are considered, twists also serve as starproducts that accordingly quantize representation…

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 consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the…

Let $V$ be a simple, rational, $C_2$-cofinite vertex operator algebra and $G$ a finite group acting faithfully on $V$ as automorphisms, which is simply called a rational vertex operator algebra with a $G$-action. It is shown that the…

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights.…

Let $X$ be a compact Riemann surface, $\Gamma$ a finite group of automorphisms of $X$ and $G$ a connected reductive complex Lie group with center $Z$. If we equip this data with a homomorphism $\theta:\Gamma\to\text{Aut}(G)$ and a 2-cocycle…

We introduce a twisted fiber bundle construction of quantum CSS codes over group algebras \(R=\mathbb F_2[G]\), where each base generator carries a generator-dependent \(R\)-linear fiber twist satisfying a flatness condition. This…

In this paper, we determine all simple restricted modules over the mirror Heisenberg-Virasoro algebra ${\mathfrak{D}}$, and the twisted Heisenberg-Virasoro algebra $\bar\mathfrak{D}$ with nonzero level. As applications, we characterize…

Let $K$ be an algebraically closed field of characteristic zero, and let $G$ be a connected reductive algebraic group over $K$. We address the problem of classifying triples $(G,H,V)$, where $H$ is a proper connected subgroup of $G$, and…