| Maps Preserving Zero Lie Brackets on a Maximal Nilpotent Subalgebra of the Symplectic Algebra |
| Received:October 26, 2009 Revised:May 31, 2010 |
| Key Words:
maximal nilpotent subalgebra zero Lie brackets symplectic algebra.
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| Fund Project:Supported by the Doctor Foundation of Henan Polytechnic University (Grant No.B2010-93), the Natural Science Research Program of Education Department of Henan Province (Grant No.2011B110016), the Natural Science Foundation of Henan Province (Grant No.11230 |
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| Abstract: |
| Let $F$ be a field with char $F\neq2$, $l$ a maximal nilpotent subalgebra of the symplectic algebra $\sp(2m,F)$. In this paper, we characterize linear maps of $l$ which preserve zero Lie brackets in both directions. It is shown that for $m\geq 4$, a map $\varphi$ of $l$ preserves zero Lie brackets in both directions if and only if $\varphi=\psi_{c}\sigma_{T_0}\lambda_{\alpha}\phi_{d}\eta_{f}$, where $\psi_{c}, \sigma_{T_0}, \lambda_{\alpha}, \phi_{d}, \eta_{f}$ are the standard maps preserving zero Lie brackets in both directions. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.05.008 |
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