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 alg...

Using the concept of codes on ordered sets introduced by Brualdi, Graves and Lawrence, we consider perfect codes on the ordinal sum of two ordered sets, the standard ordered sets and the disjoint sum of two chains. In the classical coding theory all perfect codes are completely described in terms of parameters (cf. [2, 3]). They are mathematically interesting structures. Brualdi et al. [1] rece...

The various relations between q-deformed oscillators algebras and the q-deformed su(2) algebras are discussed. In particular, we exhibit the similarity of the q-deformed su(2) algebra obtained from q-oscillators via Schwinger construction and those obtained from q-Holstein-Primakoff transformation and show how the relation between su √ q (2) and Hong Yan q-oscillator can be regarded as an speci...