Related papers: Support varieties for modules over stacked monomia…

For any triple $(\mu,\lambda,\alpha)$ of complex numbers and an $\mathfrak a$-module ${V}$, a class of non-weight modules $\mathcal{M}\big(V,\mu,\Omega(\lambda,\alpha)\big)$ over the Virasoro algebra $\mathcal L$ is constructed in this…

Let $\mathbb{K}$ be an algebraically closed field of characteristic $0$. We study a monoidal category $\mathbb{T}_\alpha$ which is universal among all symmetric $\mathbb{K}$-linear monoidal categories generated by two objects $A$ and $B$…

Let G be a simple classical algebraic group over an algebraically closed field of positive characteristic. We describe the support variety of a simple G-module over the r-th Frobenius kernel of G, in terms of its calculation over the first…

For any dg algebra $A$ we construct a closed model category structure on dg $A$-modules such that the corresponding homotopy category is compactly generated by dg $A$-modules that are finitely generated and free over $A$ (disregarding the…

A monomial basis and a filtration of subalgebras for the universal enveloping algebra $U(g_l)$ of a complex simple Lie algebra $g_l$ of type $A_l$ is given in this note. In particular, a new multiplicity formula for the Weyl module…

Let $mathfrak{g}$ be a restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. Let $\mathfrak{u}(\mathfrak{g})$ denote the restricted enveloping algebra of $\mathfrak{g}$. In this paper we prove that the…

Gabber's Theorem claims that the singular support of a D-module is involutive. We show how to give a conceptually clear proof of this in the context of Hochschild Homology and Cohomology of abelian categories.

I. Panin proved in the nineties that the algebraic K-theory of twisted projective homogeneous varieties can be expressed in terms of central simple algebras. Later, Merkurjev and Panin described the algebraic K-theory of toric varieties as…

The stable module category of a selfinjective algebra is triangulated, but need not have any nontrivial $t$-structures, and in particular, full abelian subcategories need not arise as hearts of a $t$-structure. The purpose of this paper is…

We are concerned with the problem of the stability of the syzygy bundles associated to base point free vector spaces of forms of the same degree d on the projective space of dimension n. We deduce directly, from Mark Green's vanishing…

Let $A$ be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra $\mathcal{O}(G)$ of a semisimple algebraic group $G$. It is shown that if $A$ admits a suitably non-degenerate comodule $V$ and the induced $G$-module…

For any two complex numbers $a$ and $b$, $\mathcal{V} ir(a,b)$ is a central extension of $\mathcal{W}(a,b)$ which is universal in the case $(a,b)\neq (0,1)$, where $\mathcal{W}(a,b)$ is the Lie algebra with basis $\{L_n,W_n\mid n\in\Z\}$…

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…

Consider a field k of characteristic p > 0, G_r the r-th Frobenius kernel of a smooth algebraic group G, DG_r the Drinfeld double of G_r, and M a finite dimensional DG_r-module. We prove that the cohomology algebra H*(DG_r,k) is finitely…

A commutative associative algebra $A$ over ${\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an…

For any Kac-Moody group $G$ with Borel $B$, we give a monoidal equivalence between the derived category of $B$-equivariant mixed complexes on the flag variety $G/B$ and (a certain completion of) the derived category of $B^\vee$-monodromic…

A description is given of those sequences ${\Bbb S}= (S(0),S(1),\dots,S(l))$ of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors…

Let g=g_{0} \oplus g_{1} be a classical Lie superalgebra and F be the category of finite dimensional g-supermodules which are semisimple over g_{0}. In this paper we investigate the homological properties of the category F. In particular we…

Let \(\Lambda\) be a finite-dimensional Koszul algebra with Koszul dual \(\Lambda^!\). We establish derived Koszul dualities at the level of bounded derived categories, both in the graded setting \(\mathsf{D}^{b}(\Lambda\textup{-gmod})\)…

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as…