Related papers: Extensions of Verma modules
In this paper, we investigate extensions between graded Verma modules in the BGG category $\mathcal{O}$. In particular, we determine exactly which information about extensions between graded Verma modules is given by the coefficients of the…
We give a geometric categorification of the Verma modules $M(\lambda)$ for quantum $\mathfrak{sl}_2$.
Computing the extensions between Verma modules is in general a very difficult problem. Using Soergel bimodules, one can construct a graded version of the principal block of Category $\mathcal{O}$ for any finite coxeter group. In this…
Irreducibilities of Verma modules over a class of Block type Lie algebras are completely determined. The approach developed in the present paper can be used to deal with non-weight modules.
A recent result of N. Abe implies that the Gabber-Joseph conjecture is true for the first-degree extensions between Verma modules with regular integral highest weights.
In this work we develop some categorical aspects of the double structure of a module.
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.
We introduce a notion of Krein C*-module over a C*-algebra and more generally over a Krein C*-algebra. Some properties of Krein C*-modules and their categories are investigated.
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…
We establish connections between silting and tilting objects in an abelian category $\mathcal{B}$ and those in a cleft extension $\mathcal{A}$ of $\mathcal{B}$, which provides a method for constructing more silting and tilting objects. Then…
Let $\mathfrak g(G,\lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $\lambda\neq-1$ and an additive subgroup $G$ of $\mathbb C$. For a total order on $G$ that is compatible with addition,…
We give a full classification, in terms of periodic skew diagrams, of irreducible semisimple modules in category O for the degenerate double affine Hecke algebra of type A which can be realized as submodules of Verma modules.
Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.
In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sums.
We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…
This is the author's diploma thesis. In the first part of the thesis the algebra structure on the Ext-spaces Ext^k(M(x), M(y)) of Verma modules M(x) and M(y) in the parabolic category O for the case of the parabolic subalgebras gl(n) x…
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
In this paper we investigate extended modules for a special class of Ore extensions. We will assume that $R$ is a ring and $A$ will denote the Ore extension $A:=R[x_1,\dots,x_n;\sigma]$ for which $\sigma$ is an automorphism of $R$,…
In this paper, some new characterizations on Gorenstein projective, injective and flat modules over commutative noetherian local ring are given.
We classify the module categories over the double (possibly twisted) of a finite group.