DISCRETE AND CONTINUOUS GRADED CONTRACTIONS OF LIE-ALGEBRAS AND SUPERALGEBRAS

Grading preserving contractions of Lie algebras and superalgebras of any type over the complex number field are defined and studied. Such contractions fall naturally into two classes: the Wigner-Inonu-like continuous contractions and new discrete contractions. A general method is described for any Abelian grading semigroup and any Lie algebra or superalgebra admitting such a grading. All contractions preserving Z2-, Z3-, and Z2 x Z2-gradings are found. Examples of these gradings and contractions for the simple Lie algebra A2, affine Kac-Moody algebra A1(1) and the simple superalgebra osp(2,1) are shown.