Related papers: On the support varieties of Demazure modules

We study representations of the locally unital and locally finite dimensional algebra $B$ associated to the Brauer category $\mathcal B(\delta_0)$ with defining parameter $\delta_0$ over an algebraically closed field $K$ with characteristic…

Following Nazarov's suggestion~\cite{Naz1}, we refer to the cyclotomic Nazarov-Wenzl algebra as the cyclotomic Brauer algebra. When the cyclotomic Brauer algebra is isomorphic to the endomorphism algebra of $M_{I_i, r}$-- the tensor product…

We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along…

The present paper mainly considers the representation type of the enveloping algebra of monomial algebra. Let $A$ be a monomial algebra and $A^e= A\otimes_{\mathrm{l}\!\mathrm{k}} A^{\mathrm{op}}$ its enveloping algebra. It is shown that…

The author constructs the moduli of representations whose images generate the subalgebra of upper triangular matrices (up to inner automorphisms) of the full matrix ring for any groups and any monoids.

We describe the structure of projective indecomposable modules for the subalgebra consisting of the elements of degree 0 in the hyperalgebra of the $r$-th Frobenius kernel for the algebraic group ${\rm SL}_2(k)$, using the primitive…

In the first part of this paper we present explicit formulas for primitive idempotents in arbitrary Frobenius algebras using the entries of representing matrices coming from projective indecomposable modules with respect to a certain choice…

For a split quasireductive supergroup $G$ defined over a field, we study structure and representation of Frobenius kernels $G_r$ of $G$ and we give a necessary and sufficient condition for $G_r$ to be unimodular in terms of the root system…

We show that bounded type implies finite type for a constructible subcategory of the module category of a finitely generated algebra over a field, which is a variant of the first Brauer-Thrall conjecture. A full subcategory is constructible…

In this paper we give a module-theoretic description of the isomorphism classes of abelian varieties $A$ isogenous to $B^r$, where the characteristic polynomial $g$ of Frobenius of $B$ is an ordinary square-free $q$-Weil polynomial, for a…

Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…

We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…

We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes $Z^\bullet$ of modules for a profinite group $G$ over a complete local Noetherian ring $A$ of positive residue characteristic…

We compute the number of orbits of pairs in a finitely generated torsion module (more generally, a module of bounded order) over a discrete valuation ring. The answer is found to be a polynomial in the cardinality of the residue field whose…

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $\theta$ and let $\mathfrak{g}[t]$ be the corresponding current algebra. In this paper, we consider the $\mathfrak{g}[t]$-stable Demazure modules…

We describe the support of $F$-finite $F$-modules over polynomial rings $R$ of prime characteristic. Our description yields an algorithm to compute the support of such modules; the complexity of our algorithm is also analyzed. To the best…

We define and study twisted support varieties for modules over an Artin algebra, where the twist is induced by an automorphism of the algebra. Under a certain finite generation hypothesis, we show that the twisted variety of a module…

We describe locally the representation varieties of fundamental groups for smooth complex varieties at representations coming from the monodromy of a variation of mixed Hodge structure. Given such a manifold $X$ and such a linear…

For a point $x_0$ in a Shimura variety attached to a Shimura datum of Hodge type $(G,X)$, we have an associated abelian scheme $A_0$. Fixing a non-empty finite set $\mathcal{S}$ of primes, we consider the simultaneous supersingular…

Let $G$ be a finite group and $p$ be a prime. We study the kernel of the map, between the Burnside ring of $G$ and the Grothendieck ring of $\mathbb{F}_p[G]$-modules, taking a $G$-set to its associated permutation module. We are able, for…