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COMPLEX STRUCTURES ON STRATIFIED LIE ALGEBRAS

Part of: Lie groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  19 April 2022

JUNZE ZHANG Open the ORCID record for JUNZE ZHANG [Opens in a new window]
JUNZE ZHANG*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
*
e-mail: [email protected]
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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.

Keywords

complex structurestratified Lie algebranilpotent Lie algebraJ-invariant central series

MSC classification

Primary: 22E25: Nilpotent and solvable Lie groups
Secondary: 20G07: Structure theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 2 , October 2022 , pp. 320 - 332
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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