Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-02-02
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 8 pages; Invited lecture at the BARUT Memorial Conference on Group Theory in Physics (Edirne, Turkey, 21-27 December 19
Scientific paper
Contractions (and graded contractions) of Lie algebra, Lie bialgebra and Hopf algebra are discussed. It is noticed the fundamental role of E.In{\"o}n{\"u} and E.P.Wigner idea of degenerate transformations. A constructive algorithm for description of contractions of quantum Cayley-Klein algebras $ so_{z}(n+1; {\bf j}) $ with different choice of the set of primitive operators is suggested. For nonsemisimple quantum algebras it gives nonisomorphic Hopf algebras. From physical point of view this algorithm gives the different physical interpretations of primitive operators for mathematically the same nonsemisimple quantum algebra. The case of $ so_{z}(3; {\bf j}) $ is regarded in detail.
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