Related papers: The Steinberg linkage class for a reductive algebr…

Let R > S be finite Frobenius rings for which there exists a trace map T from R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is an S-linear subring-subcode of a left linear code over R. We consider functions f…

Let N be a square-free positive integer and let f be a newform of weight 2 on \Gamma_0(N). Let A denote the abelian subvariety of J_0(N) associated to f and let m be a maximal ideal of the Hecke algebra T that contains Ann_T(f) and has…

The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…

A correspondence functor is a functor from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring. We determine exactly which simple correspondence functors are projective. Moreover,…

Let G be a simple complex algebraic group and let K be a reductive subgroup of G such that the coordinate ring of G/K is a multiplicity free G-module. We consider the G-algebra structure of C[G/K], and study the decomposition into…

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated…

Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V…

For a split reductive group $G$ over a finite extension $L$ of ${\mathbb Q}_p$, and a parabolic subgroup $P \subset G$ we examine functorial properties of the functors ${\mathcal F}^G_P$ introduced in \cite{OS2}. We discuss the aspects of…

Given a Frobenius category $\mathcal{F}$ satisfying certain finiteness conditions, we consider the localization of its Hall algebra $\mathcal{H(F)}$ at the classes of all projective-injective objects. We call it the {\it "semi-derived Hall…

We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring $R$ yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective…

Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two $\sigma$-compact open projections. It is proved that there is a continuous path of unitaries in ${\tilde A}$ which connects open sub-projections of $p$ which is…

We compute projective dimension of translated simple modules in the regular block of the BGG category $\mathcal{O}$ in terms of Kazhdan-Lusztig combinatorics. This allows us to determine which projectives can appear at the last step of a…

We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective, then its underlying module over the the base ring is Gorenstein projective; the converse holds if the Frobenius extension is either…

In the first part of this paper the projective dimension of the structural modules in the BGG category $\mathcal{O}$ is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an…

Let ${\mathfrak g}$ be a finite dimensional Lie algebra over a field of characteristic 0, with solvable radical ${\mathfrak r}$ and nilpotent radical ${\mathfrak n}=[{\mathfrak g},{\mathfrak r}]$. Given a finite dimensional ${\mathfrak…

We study the question of the existence of a Waldhausen category on any (relative) abelian category in which the contractible objects are the (relatively) projective objects. The associated $K$-theory groups are "stable algebraic…

Let $G$ be a group. A ring $R$ is called a graded ring (or $G$-graded ring) if there exist additive subgroups $R_{\alpha }$ of $R$ indexed by the elements $\alpha \in G$ such that $R=\bigoplus_{\alpha \in G}R_{\alpha }$ and $R_{\alpha…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We construct a co-$t$-structure on the derived category of coherent sheaves on the nilpotent cone $\mathcal{N}$ of a reductive group, as well as on the derived category of coherent sheaves on any parabolic Springer resolution. These…

Let $\mathfrak{g}$ be a simple complex Lie algebra of classical type with a Cartan subalgebra $\mathfrak{h}$. We fix a standard parabolic subalgebra $\mathfrak{p}\supset \mathfrak{h}$. The socular simple modules are just those highest…