Allografts continue to be used in clinical neurotransplantation studies; hence, it is crucial to understand the mechanisms that govern allograft tolerance. We investigated the impact of… (More)

In 1984, Victor Kac [K4] suggested an approach to a description of central elements of a completion of U(g) for any Kac-Moody Lie algebra g. The method is based on a recursive procedure. Each step is… (More)

We define a notion of ghost centre of a Lie superalgebra g = g0 ⊕ g1 which is a sum of invariants with respect to the usual adjoint action (centre) and invariants with respect to a twisted adjoint… (More)

We define an analogue of Shapovalov forms for Q-type Lie superalgebras and factorize the corresponding Shapovalov determinants which are responsible for simplicity of highest weight modules. We apply… (More)

In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type… (More)

1.1. In [PS1], I. Penkov and V. Serganova show that the category of representations of a basic classical Lie superalgebra g of type I with a fixed typical central character is equivalent to the… (More)

We find necessary and sufficient conditions of irreducibility of vacuum modules over affine Lie algebras and superalgebras. From this we derive conditions of simplicity of minimal W -algebras.… (More)

0.1. Let g be a complex finite-dimensional contragredient Lie superalgebra. These algebras were classified by V. Kac in [K1] and the list (excluding Lie algebras) consists of four series: A(m|n),… (More)

Weyl denominator identity for the affinization of a basic Lie superalgebra with non-zero Killing form was formulated by V. Kac and M. Wakimoto and was proven by them for the defect one case. In this… (More)

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra ĝ 6= A(2k, 2l). We obtain the character formula for a… (More)