代数结构的收缩与Cayley-Klein和Hopf结构的不同耦合
Contraction of Algebraical Structures and Different Couplings of Cayley-Klein and Hopf Structures
摘要：
讨论了李代数、李双代数和Hopf代数的压缩（和分次压缩）.注意到E.In{<$}n{<$}和E. P. Wigner关于简并变换的基本思想。给出了一种构造性算法，用于描述不同本原算子集选择的量子Cayley-Klein代数$ so_{z}(n+1; {\bf j}) $的压缩.对于非半单量子代数，给出了非同构的Hopf代数.该算法从物理角度给出了数学上相同的非半单量子代数的本原算符的不同物理解释。详细讨论了$ so_{z}(3; {\bf j}) $的情况。
英文摘要：
Contractions (and graded contractions) of Lie algebra, Lie bialgebra and Hopf algebra are discussed. It is noticed the fundamental role of E.In{ö}n{ü} 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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