Related papers: Projective modules of $0$-Schur algebras
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. First we will give a criterion for Ext-vanishing for…
We describe recent work on preprojective algebras and moduli spaces of their representations. We give an analogue of Kac's Theorem, characterizing the dimension types of indecomposable coherent sheaves over weighted projective lines in…
The immaculate Hecke poset was introduced and investigated by Niese, Sundaram, van Willigenburg, Vega and Wang, who established the full poset structure, and determined modules for the 0-Hecke algebra action on immaculate and row-strict…
Let $K$ be any field, and let $E$ be any graph. We explicitly construct the projective resolution of simple left modules over the Leavitt path algebra $L_K(E)$ associated to cycles and irreducible polynomials. Then we study the dimension of…
By using methods developed in arXiv:math/0602181 we study the irreducibility of certain Wakimoto modules for $\widehat{sl_2}$ at the critical level. We classify all $\chi \in {\Bbb C}((z))$ such that the corresponding Wakimoto module…
The modular curves serve as excellent objects for testing conjectures in arithmetic geometry. They possess a natural geometric definition in contrast with rather nontrivial structure. On the other hand, they are well-studied from the…
Let $\mathscr{H}_n$ denote the Iwahori-Hecke algebra corresponding to the symmetric group $\mathfrak{S}_n$. We set up a Green correspondence for bimodules of these Hecke algebras, and a Brauer correspondence between their blocks. We examine…
Generalizing Jones's notion of a planar algebra, we have previously introduced an A_2-planar algebra capturing the structure contained in the double complex pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system.…
We describe the wall and chamber structure of a special biserial algebra whose module category is equivalent to the category of (middle) perverse sheaves on the complex projective space $\mathbb{P}^n$. In particular, by the well known…
In this paper we study irreducible modules for loop of $A\rtimes DerA$ with finite dimensional weight spaces. In particular, we show that Larsson's constructed modules of tensor fields exhausted all irreducible modules.
We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups.
In this paper, Whittaker modules for the Schr\"odinger-Virasoro algebra $\mathfrak{sv}$ are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. $\mathfrak{sv}$ has a triangular decomposition according…
In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Let ${p > 2}$ be an odd prime and ${G = SL_2(\mathbb{F}_p)}$. Denote the subgroup of upper triangular matrices as $B$. Finally, let ${\mathbb{F}}$ be an algebraically closed field of characteristic ${p}$. The Green correspondence gives a…
We introduce a general method for constructing modules for $0$-Hecke algebras and supermodules for $0$-Hecke-Clifford algebras from diagrams of boxes in the plane, and give formulas for the images of these modules in the algebras of…
We characterize the canonical algebras such that for all dimension vectors of homogeneous modules the corresponding module varieties are complete intersections (respectively, normal). We also investigate the sets of common zeros of…
We study the splitting-type of the bi-modules of principal parts (Grothendiecks analogue of jet-bundles in algebraic geometry) as left and right O-module on the projective line in positive characteristic, and obtain explicit examples where…
In this paper, we study the structure of Shen-Larsson modules over the Hamiltonian Lie algebra, also known as the Lie algebra of Hamiltonian vector fields on a torus. We establish necessary and sufficient conditions for the irreducibility…