On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras

Fernando Szechtman; Leandro Cagliero

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On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras

机译：原始元素定理在联想和李代数表示理论中的应用

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We describe of all finitedimensional uniserial representations of a commutative associative(resp. abelian Lie) algebra over a perfect (resp. sufficientlylarge perfect) field. In the Lie case the size of the fielddepends on the answer to following question, considered and solvedin this paper. Let $K/F$ be a finite separable field extensionandlet $x,yin K$. When is $F[x,y]=F[alpha x+eta y]$ for somenon-zero elements $alpha,etain F$?

机译：我们描述了一个理想域（分别是足够大的理想域）上的可交换（代阿贝尔李）代数的所有有限维无序列表示。在Lie情况下，字段的大小取决于以下问题的答案，本文将予以考虑和解决。令$ K / F $为有限的可分离字段扩展，并让$ x，yK $。对于某些非零元素$ alpha，何时$ F [x，y] = F [alpha x + eta y] $，得到F $？

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《Canadian mathematical bulletin》 |2014年第2014期|共页
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Fernando Szechtman; Leandro Cagliero;
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中图分类数学;
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1. On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras [J] . Leandro Cagliero, Fernando Szechtman Canadian Mathematical Bulletin . 2014,第4期

机译：原始元素定理在联想和李代数表示理论中的应用
2. Theorems on the Jordan-Schwinger Representations of Lie Groups and its Application to the Algebraic Hamiltonian for Vibron Model of Diatomic Molecules [J] . Dong J. Lee, Shoon K. Kim Bulletin of the Korean Chemical Society . 1990,第4期

机译：李群的Jordan-Schwinger表示定理及其在双原子分子Vibron模型代数哈密顿量中的应用
3. THE LIE ALGEBRA OF SKEW-SYMMETRIC ELEMENTS AND ITS APPLICATION IN THE THEORY OF JORDAN ALGEBRAS [J] . S. R. Sverchkov Siberian Mathematical Journal . 2010,第3期

机译：对称对称元素的李代数及其在约旦代数理论中的应用
4. Algorithms for primitive elements of free Lie algebras and Lie superalgebras [C] . Alexander A. Mikhalev, Andrej A. Zolotykh International symposium on Symbolic and algebraic computation . 1996

机译：自由李代数和李超代数本原元素的算法
5. Three contributions to topology, algebraic geometry and representation theory: Homological finiteness of abelian covers, algebraic elliptic cohomology theory and monodromy theorems in the elliptic setting. [D] . Yang, Yaping. 2014

机译：对拓扑，代数几何和表示理论的三个贡献：阿贝尔封面的同调有限性，代数椭圆同调理论和椭圆环境中的一峰定理。
6. Ideals and primitive elements of some relatively free Lie algebras [O] . Naime Ekici, Zerrin Esmerligil, Dilek Ersalan -1

机译：一些相对自由的李代数的理想和本原元素
7. 3 ON THE THEOREM OF THE PRIMITIVE ELEMENT WITH APPLICATIONS TO THE REPRESENTATION THEORY OF ASSOCIATIVE AND LIE ALGEBRAS [O] . Leandro Cagliero, Fernando Szechtman 2016

机译：3关于原始元素的定理及其在关联和李代数表示理论中的应用
8. A Rigidity Theorem for Subalgebras of Lie and Associative Algebras [R] . Richardson, R. W. 1965

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On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras

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