Generalized deformed algebras F(A1) and their applications

Generalized deformation of A1 is proposed. Some generalized deformed algebras F(A1) and their unitary representations are discussed in detail. F(A1) involves not only Lie algebras SU(2), SU(1,1), E2 and boson algebra as special cases, but also quantum algebras SUq(2), SUq(1,1), q-boson algebra, and a large class of other nonlinear algebras. It is found that these algebras can be mapped from one type to another by generalized deforming functionals in some cases. Possible applications in physical problems are outlined. Some examples are also given as illustrations.