We find the free field construction of basic $W$-current and screening currents for deformed $W$-superalgebra ${\cal W}_{q,t}\bigl(A(M,N)\bigr)$ associated with Lie superalgebra type $A(M,N)$. Using this construction, we introduce higher $W$-currents obtain a closed set quadratic relations among them. These are independent choice Dynkin-diagrams $A(M,N)$, though not. This allows us to define by...

The superalgebra of [Formula: see text]-graded supersymmetric quantum mechanics is shown to be realizable in terms a single bosonic degree freedom. Such an approach directly inspired by description the corresponding framework Calogero–Vasiliev algebra or, more generally, generalized deformed oscillator algebra. In case superalgebra, central element text] has property distinguishing between dege...

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 category of representations of the even part g0 with a suitable central character. A similar result for type II was proven by I. Penkov in [P] for “generic” central characters. The aim of this paper is t...

We study the superalgebra of the M-theory on a fully supersymmetric pp-wave. We identify the algebra as the special unitary Lie superalgebra, su(2|4 ; 2, 0) or su(2|4 ; 2, 4), and analyze its root structure. We discuss the typical and atypical representations deriving the typicality condition explicitly in terms of the energy and other four quantum numbers. We classify the BPS multiplets preser...

In this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivalence conjugation classes. For some of the subalgebras, the invariants have a non-standard structure. For nine selected subalgebras, we use the symme...

We study of the category O for the queer Lie superalgebra q(n), and the corresponding block decomposition induced by infinitesimal central characters. In particular, we show that the so-called typical blocks correspond to standardly stratified algebras, in the sense of Cline, Parshall and Scott. By standard arguments for Lie algebras, modified to the superalgebra situation, we prove that these ...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...