Discussion on the Homology Theory of Lie Algebras  

作　　者：Lilong Kang Yu Wang Caiyu Du Lilong Kang;Yu Wang;Caiyu Du(College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China)

机构地区：[1]College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第7期2367-2376,共10页应用数学与应用物理（英文）

摘　　要：Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).

关 键 词：Lie Algebra Differential Sequence Differential Fractional Algebra COHOMOLOGY 

分 类 号：O15[理学—数学]