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Millionschikov, D.V. (2014) Complex Structures on Nilpotent Lie Algebras and Descending Central Series. arXiv: Rings and Algebras.

has been cited by the following article:

• 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.