Related papers: Elementary Equivariant Modules

We begin the study of a tilting theory in certain truncated categories of modules $\mathcal G(\Gamma)$ for the current Lie algebra associated to a finite-dimensional complex simple Lie algebra, where $\Gamma = P^+ \times J$, $J$ is an…

In this paper, we examine the unimodality and strict unimodality of certain formal bivariate Laurent series with non-negative coefficients. We show that the sets of these formal bivariate Laurent series form commutative semirings under the…

We survey the state of the art on amalgamation in varieties of semilinear residuated lattices. Our discussion emphasizes two prominent cases from which much insight into the general picture may be gleaned: idempotent varieties and their…

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

An FI- or an OI-module $\mathbf{M}$ over a corresponding noetherian polynomial algebra $\mathbf{P}$ may be thought of as a sequence of compatible modules $\mathbf{M}_n$ over a polynomial ring $\mathbf{P}_n$ whose number of variables depends…

We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between…

Given a finite-dimensional module, $V$, for a finite-dimensional, complex, semi-simple Lie algebra $\lie g$ and a positive integer $m$, we construct a family of graded modules for the current algebra $\lie g[t]$ indexed by simple $\CC\lie…

Let D be a division ring such that the number of conjugacy classes in the multiplicative group D^* is equal to the power of D^*. Suppose that H(V) is the group GL(V) or PGL(V), where V is an infinite-dimensional vector space over D. We…

We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an…

Let $R$ be the associative $k$-algebra generated by two elements $x$ and $y$ with defining relation $yx=1$. A complete description of simple modules over $R$ is obtained by using the results of Irving and Gerritzen. We examine the short…

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…

Let $\Lambda$ be a graded self-injective algebra. We describe its smash product $\Lambda# k\mathbb Z^*$ with the group $\mathbb Z$, its Beilinson algebra and their relationship. Starting with $\Lambda$, we construct algebras with finite…

Let $F$ be a finite extension of $\mathbb{Q}_p$, let $\Omega_F$ be Drinfeld's upper half-plane over $F$ and let $G^0$ the subgroup of $GL_2(F)$ consisting of elements whose determinant has norm $1$. By working locally on $\Omega_F$, we…

It is well known that the moduli space of flat connections on a trivial principal bundle MxG, where G is a connected Lie group, is isomorphic to the representation variety Hom(\pi_1(M), G)/G. For a tiling T, viewed as a marked copy of R^d,…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geq 0$ and let $V$ be an irreducible rational $G$-module with highest weight $\lambda$. When $V$ is self-dual, a basic question to ask…

Let $\Lambda$ be an artin algebra. We are going to consider full subcategories of $\mod\Lambda$ closed under finite direct sums and under submodules with infinitely many isomorphism classes of indecomposable modules. The main result asserts…

Let $\mathbf{k}$ be an algebraically closed field, let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra, and let $\widehat{\Lambda}$ be the repetitive algebra of $\Lambda$. For the stable category of finitely generated left…

Basic modules of McLain groups $M=M(\Lambda,\leq, R)$ are defined and investigated. These are (possibly infinite dimensional) analogues of Andr\'e's supercharacters of $U_n(q)$. The ring $R$ need not be finite or commutative and the field…

In this paper, we show that for an algebra $\Lambda$ with radical square zero and an indecomposable $\Lambda$-module $M$ such that $\Lambda$ is Gorenstein of finite type or $\tau M$ is $\tau$-rigid, $M$ is $\tau$-rigid if and only if the…

Let $A = K[[X_1,\cdots,X_n]]$ and let $\mathfrak{m} = (X_1,\cdots,X_n)$. Let $M$ be a Cohen-Macaulay $A$-module of codimension $p$. In this paper we give a necessary and sufficient condition for the associated graded module…