Related papers: Type A blocks of super category O

We classify the blocks, compute the Verma flags of tilting and projective modules in the BGG category $\mathcal O$ for the exceptional Lie superalgebra $G(3)$. The projective injective modules in $\mathcal O$ are classified. We also compute…

In this paper we describe the the category of Lie algebras of group algebras and the category of Plesken Lie algebras and explore the categorical relations between them. Further we provide the examples of the Lie algebra of the group…

This article explores the structure theory of compatible generalized derivations of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $\omega$-Lie algebra can be embedded…

We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…

We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…

Let $\mathcal{U}$ be a braided tensor category, typically unknown, complicated and in particular non-semisimple. We characterize $\mathcal{U}$ under the assumption that there exists a commutative algebra $A$ in $\mathcal{U}$ with certain…

In this paper we study the finite W-algebra for the queer Lie superalgebra Q(n) associated with the non-regular even nilpotent coadjoint orbits in the case when the corresponding nilpotent element has Jordan blocks each of size l. We prove…

Let $U_\zeta$ be a Lusztig quantum enveloping algebra associated to a complex semisimple Lie algebra $\mathfrak g$ and a root of unity $\zeta$. When $L,L'$ are irreducible $U_\zeta$-modules having regular highest weights, the dimension of…

Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data…

We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…

Let $G$ be a finite group of Lie type. In studying the cross-characteristic representation theory of $G$, the (specialized) Hecke algebra $H=\End_G(\ind_B^G1_B)$ has played a important role. In particular, when $G=GL_n(\mathbb F_q)$ is a…

We give a new proof of the fact that the super Yangian of general linear Lie superalgebra is isomorphic to the finite W-superalgebra of the general linear Lie superalgebra associated to a rectangular nilpotent element.

Let $k$ be a field and $A$ a finite-dimensional $k$-algebra of global dimension $\leq 2$. We construct a triangulated category $\Cc_A$ associated to $A$ which, if $A$ is hereditary, is triangle equivalent to the cluster category of $A$.…

We show that a quantum super matrix in standard format is invertible if and only if its block matrices of even entries are invertible. We prove the q-analog of the well-known formula for the Berezinian.

We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type…

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible…

In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, $A$, over a ring of scalars $\Phi$ with $1/2\in \Phi$, if $L$ is a Lie…

Turner's Conjecture describes all blocks of symmetric groups and Hecke algebras up to derived equivalence in terms of certain double algebras. With a view towards a proof of this conjecture, we develop a general theory of Turner doubles. In…

Varagnolo and Vasserot conjectured an equivalence between the category O for CRDAHA's and a subcategory of an affine parabolic category O of type A. We prove this conjecture. As applications, we prove a conjecture of Rouquier on the…

The article concerns the subalgebra U_v^+(w) of the quantized universal enveloping algebra of the complex Lie algebra sl_{n+1} associated with a particular Weyl group element of length 2n. We verify that U_v^+(w) can be endowed with the…