DEFORMATION OF LIE-ALGEBRAS IN A NON-CHEVALLEY BASIS AND EMBEDDING OF Q-ALGEBRAS

A deformation scheme for Lie algebras in a basis which manifestly exhibits for q = 1 the content of a singular subalgebra is presented. This scheme allows to build up 'embedding' chains of q-algebras which can be physically interesting. In the present paper the case when the rank of the subalgebra is one unit less than the rank of the algebra is studied and explicit constructions of the algebras are given in terms of q-bosonic and/or q-fermionic oscillators.