We propose a recipe to construct matrix representations of Nambu– Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.

The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V. Kac is refined. In reality these representations are not just induced from a polarization but are twisted ones, as infinite dimensional representations of solvable Lie algebras. Various cases of irreducibility (general and of type Q) are classified.

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schrr odinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by rst-order matrix diierential operators. We have classiied inequivalent representations of the Lie alg...