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COMPLEX STRUCTURES ON STRATIFIED LIE ALGEBRAS
Published online by Cambridge University Press: 19 April 2022
Abstract
We investigate some properties of complex structures on Lie algebras. In particular, we focus on nilpotent complex structures that are characterised by suitable J-invariant ascending or descending central series,
$\mathfrak {d}^{\,j}$
and
$\mathfrak {d}_j$
, respectively. We introduce a new descending series
$\mathfrak {p}_j$
and use it to prove a new characterisation of nilpotent complex structures. We also examine whether nilpotent complex structures on stratified Lie algebras preserve the strata. We find that there exists a J-invariant stratification on a step
$2$
nilpotent Lie algebra with a complex structure.
MSC classification
Secondary:
20G07: Structure theory
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 106 , Issue 2 , October 2022 , pp. 320 - 332
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
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