TITLE:
Discussion on the Complex Structure of Nilpotent Lie Groups Gk
AUTHORS:
Caiyu Du, Yu Wang
KEYWORDS:
Almost Complex Structure, Nilpotent Lie Group, Nilpotent Lie Algebra
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.14 No.6,
June
11,
2024
ABSTRACT: 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.