We present in detail the classification of the finite dimensional irreducible representations of the super Yangian associated with the Lie superalgebra gl(1|1). 1 Introduction Many new algebraic structures were discovered in the study of soluble models in statistical mechanics and quantum field theory. Amongst them the quantum groups[1][2] and Yangians[3] are particularly interesting. The forme...

We describe all locally semisimple subalgebras and all maximal subalgebras of the finitary Lie algebras gl(∞), sl(∞), so(∞), and sp(∞). For simple finite–dimensional Lie algebras these classes of subalgebras have been described in the classical works of A. Malcev and E. Dynkin.

‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...

It was proved by Montaner and Zelmanov that up to classical twisting Lie bialgebra structures on g[u] fall into four classes. Here g is a simple complex finite-dimensional Lie algebra. It turns out that classical twists within one of these four classes are in a one-to-one correspondence with the so-called quasi-trigonometric solutions of the classical Yang-Baxter equation. In this paper we give...

In this paper, we shall classify “quadratic” conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov superalgebra. Four general constructions of such pairs are given. Moreover, we shall classify such pairs related to simple Novikov algebras.

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U q [osp(1/2)] and the corresponding su-pergroup OSp q (1/2). The finite dimensional representations of the quantum su-pergroup OSp q (1/2) are readily constructed employing the said universal T-matrix and the known finite dimensional representations of the dually related deformed ...

We use Arkhipov’s twisting functors to show that the universal enveloping algebra of a semi-simple complex finite-dimensional Lie algebra surjects onto the space of ad-finite endomorphisms of the simple highest weight module L(λ), whose highest weight is associated (in the natural way) with a subset of simple roots and a simple root in this subset. This is a new step towards a complete answer t...