We study the representation theory of Kazama-Suzuki coset vertex operator superalgebra associated with pair a complex simple Lie algebra and its Cartan subalgebra. In case type $A_{1}$, B.L. Feigin, A.M. Semikhatov, I.Yu. Tipunin introduced another construction, which is "inverse" construction. this paper we generalize latter construction to arbitrary establish categorical equivalence between c...

Let F be the underlying base field of characteristic p > 3 and denote by W and S the even parts of the finite-dimensional generalized Witt Lie superalgebra W and the special Lie superalgebra S, respectively. We first give the generator sets of the Lie algebras W and S. Using certain properties of the canonical tori of W and S, we then determine the derivation algebra of W and the derivation spa...

We introduce a new quantum group which is a quantization of the enveloping superalgebra of a twisted affine Lie superalgebra of type Q. We study generators and relations for superalgebras in the finite and twisted affine cases, and also universal central extensions. Afterwards, we apply the FRT formalism to a certain solution of the quantum Yang-Baxter equation to define that new quantum group ...

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...

We analyse the Witten-Woronowicz's type deformations of the Lie su-peralgebra osp(2,2) and obtain a deformation parametrized by three independent parameters. For some of these algebras, finite dimensional representations are formulated in terms of a finite difference operator, providing operators that are relevant for the classification of quasi exactly solvable, finite difference equations. Si...