Discussion on the Complex Structure of Nilpotent Lie Groups Gk  

作　　者：Caiyu Du Yu Wang Caiyu Du;Yu Wang(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：《Open Journal of Applied Sciences》2024年第6期1401-1411,共11页应用科学（英文）

摘　　要：Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.

关 键 词：Almost Complex Structure Nilpotent Lie Group Nilpotent Lie Algebra 

分 类 号：O15[理学—数学]