西尔维斯特与代数不变量理论  

Sylvester and algebraic invariant theory

作　　者：金英姬[1,2] 白宏刚 

机构地区：[1]西北大学数学与科学史研究中心,陕西西安710069 [2]武警工程大学理学院,陕西西安710086

出　　处：《西北大学学报（自然科学版）》2013年第3期499-503,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10771169)

摘　　要：文中利用文献研读与历史分析法,系统研究和探讨了西尔维斯特(James Joseph Sylvester,1814—1897)创立代数不变量理论的相关思想及其贡献:西尔维斯特建立了代数不变量理论的学科语言;发明了计算不变量的一般方法——复合换位法;引进微分算子,建立了不变量零化子理论;尝试利用施图姆函数的合冲关系解决不变量的合冲问题;证明了凯莱定理。西尔维斯特的工作奠定了代数不变量的理论基础,反映了19世纪英国不变量理论研究的主要轨迹及特点。In this paper, by using the method of the literature review and historic analysis, the thought and contri- bution of the algebria invariant theory are systematically investigated and discussed, which was found by Sylvester （James Joseph Sylvester, 1814--1897 ） ： the language of the algebria invariant theory was established by Sylvester, the general method of calculating the invariants-Compound Commutants Method was devised, the theory of the in- variant annihilator was established by introducing the differential operators, the syzygy problems of the invariants was attempt to solve by using the syzygetic relations of Strurm functions, Cayley＇s theorem was proved. Sylvester＇s work laid the foundation of the algebria invariant theory, and reflected the main research track and feature of the British algebria invariant theory in the 19th century.

关 键 词：西尔维斯特(James JOSEPH SYLVESTER 1814—1897) 代数不变量 创立 

分 类 号：O11[理学—数学]