Related papers: On the Vertices of Indecomposable Modules Over Dih…

We consider the complex reflection group \( \mathcal{G} \), identified as No. 8 in the Shephard-Todd classification. In this paper, we present computations of the vector-valued invariants associated with various representations of \(…

We classify indecomposable pure injective modules over domestic string algebras, verifying Ringel's conjecture on the structure of such modules.

This paper contains the decomposition matrices for blocks of defect at most $2$ in Category $\mathcal{O}_c(W)$ of the rational Cherednik algebra when $W=E_8$ or $F_4$ with equal parameters $c=1/d$, $d>2$ a regular number of $W$. A corollary…

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group, and B is a block of kG with dihedral defect group D which is Morita equivalent to the principal…

We prove a character formula for the irreducible modules from the category $\mathcal{O}$ over the simple affine vertex algebra of type $A_n$ and $C_n$ $(n \geq 2)$ of level $k=-1$. We also give a conjectured character formula for types…

Using the fusion product of the representations of the Lie algebra $\mathfrak{sl}_2$ we construct a set of the integrable highest weight $\hat{\mathfrak{sl}_2}$-modules $L^D$, depending on the vector $D\in\mathbb{N}^{k+1}$. In a special…

We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.

Let $K$ be a differential field over $\C$ with derivation $D$, $G$ a finite linear automorphism group over $K$ which preserves $D$, and $K^G$ the fixed point subfield of $K$ under the action of $G$. We show that every finite-dimensional…

Let k be a field and n > 0. There exists a DG k-module (V,d) and various approximations d + t d_1 + t^2 d_2 + ... + t^n d_n to a differential on V[[t]], one of which is a non-trivial deformation, another is obstructed, and another is…

The rigidity degree of a generator-cogenerator determines the dominant dimension of its endomorphism algebra, and is closely related to a recently introduced homological dimension -- rigidity dimension. In this paper, we give explicit…

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…

Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.

We classify blocks in the BGG category $\mathcal O$ of modules of non-integral weights for the exceptional Lie superalgebra $D(2|1;\zeta)$. We establish various reduction methods, which connect some types of non-integral blocks of…

The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.

Let $A$ be a finite dimensional unital commutative associative algebra and let $B$ be a finite dimensional vertex $A$-algebroid such that its Levi factor is isomorphic to $sl_2$. Under suitable conditions, we construct an indecomposable…

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG with a dihedral defect group D such that there are precisely two…

Let $k$ be an algebraically closed field of characteristic $p>0$ and $G$ a finite group. We provide a description of the torsion subgroup $TT(G)$ of the finitely generated abelian group $T(G)$ of endo-trivial $kG$-modules when $p=2$ and $G$…

Let $\mathfrak g(G,\lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $\lambda\neq-1$ and an additive subgroup $G$ of $\mathbb C$. For a total order on $G$ that is compatible with addition,…

In this article, we study the derivations of group algebras of some important groups, namely, dihedral ($D_{2n}$), Dicyclic ($T_{4n}$) and Semi-dihedral ($SD_{8n}$). First, we explicitly classify all inner derivations of a group algebra…

In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is…