The nonstandard deformation U ′ q(son) for q a root of unity, Methods of Funct. Anal. Topology 6

We describe properties of the nonstandard q-deformation U ′ q (son) of the universal enveloping algebra U (son) of the Lie algebra son which does not coincide with the Drinfeld–Jimbo quantum algebra Uq(son). In particular, it is shown that there exists an isomorphism from U ′ q (son) to Uq(sln) and that finite dimensional ir-reducible representations of U ′ q (son) separate elements of this algebra. Irreducible representations of the algebras U ′ q (son) for q a root of unity q p = 1 are given. The main class of these representations act on p N-dimensional linear space (where N is a number of positive roots of the Lie algebra son) and are given by r = dim son complex parameters. Some classes of degenerate irreducible representations are also described.