束李代数及其表示理论

Bundled Lie algebras and their representation theory

首先利用极限思维,通过极限的线性化、交换图和范畴等方法,从不同角度证明了左极限李代数sl^(l)( C)与右极限李代数sl^(r)(C)同构.其次,类似地考虑左、右束李代数,结合已证结论从而证明此4个李代数相互同构,并且构造无限维向量空间.最后利用交换图简要地讨论了其同构型与表示理论.

In the report,the idea of limits was used and the linearization of limits,commutative graphs,and cat⁃egories were performed to prove the isomorphism between the left limit Lie algebra and the right limit Lie algebra from different perspectives.The left limit Lie algebra and right bundle Lie algebras,combined with the proven conclusions,were taken into accounted,it was proven that these four Lie algebras are isomorphic to each other,and an infinite dimensional vector space was constructed.Finally,the commutative graphs were used to discuss their isomorphism and representation theory.