Related papers: Dualities for Lie superalgebras

We provide a linkage principle in an arbitrary parabolic category $\mathcal O^{\mathfrak p}$ for the periplectic Lie superalgebras $\mathfrak{pe}(n)$. As an application, we classify indecomposable blocks in $\mathcal O^{\mathfrak p}$. We…

All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…

We establish a new Howe duality between a pair of quantum queer superalgebras $(\mathrm{U}_{q^{-1}}(\mathfrak{q}_n), \mathrm{U}_q(\mathfrak{q}_m))$. The key ingredient is the construction of a non-commutative analogue…

Let V be a finite-dimensional superspace and G a simple (or a ``close'' to simple) matrix Lie superalgebra, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of G-invariant elements of…

We establish that for the type I Lie superalgebras $sl(m/n)$ and $osp(2/2n)$, each Kac module admits a 1 parameter family of indecomposable double extensions. The result follows from the explicit evaluation of the $H^1$ Lie superalgebra…

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

Let $g$ be a reductive Lie algebra over a field of characteristic zero. Suppose $g$ acts on a complex of vector spaces $M$ by $i_\lambda$ and $L_\lambda$, which satisfy the identities as contraction and Lie derivative do for smooth…

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…

We reformulate the Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$ of Lie algebras of type D via the theory of canonical bases arising from quantum symmetric pairs initiated by Weiqiang Wang and the author. This is further applied…

Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized…

Polynomial representations of general linear groups and modules over Schur algebras are compared. We work over an arbitrary commutative ring and show that Schur-Weyl duality is the key for an equivalence between both categories.

In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as…

Associated to the two types of finite dimensional simple superalgebras, there are the general linear Lie superalgebra and the queer Lie superalgebra. The universal enveloping algebras of these Lie superalgebras act on the tensor spaces of…

We introduce a doubled formalism for the bosonic sector of the maximal supergravities, in which a Hodge dual potential is introduced for each bosonic field (except for the metric). The equations of motion can then be formulated as a twisted…

There is a surprising isomorphism between the quantised universal enveloping algebras of osp(1|2n) and so(2n+1). This same isomorphism emerged in recent work of Mikhaylov and Witten in the context of string theory as a T-duality composed…

We solve two problems in representation theory for the periplectic Lie superalgebra pe(n), namely the description of the primitive spectrum in terms of functorial realisations of the braid group and the decomposition of category O into…

J. G. Thompson showed that a finite group G is solvable if and only if every two -generated subgroup is solvable. Recently, Grunevald, Kunyavskii, Nikolova, and Plotkin have shown that the analogue holds for finite-dimensional Lie algebras…

We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…

We show that every integral block of category O for the general linear Lie superalgebra is equivalent to a corresponding block of category O for the queer Lie superalgebra. This implies the truth of the Kazhdan-Lusztig conjecture for the…

The purpose of this paper is to study Lie-Rinehart superalgebras over characteristic zero fields, which are consisting of a supercommutative associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in a certain way. We…