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The classification of simple structurable superalgebras of Cartan type over an algebraically closed field of characteristic 0 has been done recently by Pozhidaev and Shestakov [8]. Here we present an easy construction and quick classification of the algebras using a superalgebra version of results due to Elduque and Okubo [5] relating Lie algebras with S4-actions and structurable algebras. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we use the Etingof–Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld–Jimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that the D-J type superalgebra associated to a Lie superalgebra of type A-G, with the distinguished Cartan matrix, is isomorphic to the E-K quantization of the Lie superalgebra. The first main result in the present paper is to extend this to arbitrary Cartan matrices. This paper also contains two other main results: (1) a theorem stating that all highest weight modules of a Lie superalgebra of type A-G can be deformed to modules over the corresponding D-J type superalgebra and (2) a super version of the Drinfeld–Kohno theorem. [Copyright &y& Elsevier]

Abstract: For every semi-simple Lie algebra one can construct the Drinfeld–Jimbo algebra . This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of , Drinfeld used the KZ-equations to construct a quasi-Hopf algebra . He proved that particular categories of modules over the algebras and are tensor equivalent. Analogous constructions of the algebras and exist in the case when is a Lie superalgebra of type A-G. However, Drinfeld''s proof of the above equivalence of categories does not generalize to Lie superalgebras. In this paper, we will discuss an alternate proof for Lie superalgebras of type A-G. Our proof utilizes the Etingof–Kazhdan quantization of Lie (super)bialgebras. It should be mentioned that the above equivalence is very useful. For example, it has been used in knot theory to relate quantum group invariants and the Kontsevich integral. [Copyright &y& Elsevier]