Author(s)

Caiyu Du, Yu Wang

College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China.

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 G_k, defined by the nilpotent Lie algebra g/a_k, where g is the Lie algebra of G, and a_k is an ideal of g. Then, J gives rise to an almost complex structure J_k on G_k. 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 J_k on the nilpotent Lie group G_k, and J_k is also nilpotent.

Almost Complex Structure, Nilpotent Lie Group, Nilpotent Lie Algebra

Du, C. and Wang, Y. (2024) Discussion on the Complex Structure of Nilpotent Lie Groups G_k. Open Journal of Applied Sciences, 14, 1401-1411. doi: 10.4236/ojapps.2024.146092.