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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rationally varying polarizing subalgebras in nilpotent Lie algebras


Authors: Lawrence Corwin and Frederick P. Greenleaf
Journal: Proc. Amer. Math. Soc. 81 (1981), 27-32
MSC: Primary 17B30
MathSciNet review: 589131
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Abstract: Let $ \mathfrak{N}$ be a nilpotent Lie algebra, with (vector space) dual $ {\mathfrak{N}^{*}}$. We construct a map $ l \mapsto {\mathfrak{M}_l}$ from a Zariski-open subset of $ {\mathfrak{N}^{*}}$ to the set of subalgebras of $ \mathfrak{N}$ such that $ {\mathfrak{M}_l}$ varies rationally with $ l$, $ {\mathfrak{M}_l}$ is polarizing for $ l$, $ ({\text{Ad}}x){\mathfrak{M}_l} = {\mathfrak{M}_{l'}}(l' = {\text{A}}{{\text{d}}^ {*} }x \cdot l)$ for all $ x \in N$, and $ un{k_\infty }(l) \subseteq {\mathfrak{M}_l} \subseteq un{k_\infty }(l)$, where $ un{k_\infty }(l)$ and $ un{k_\infty }(l)$ are the canonical subalgebras introduced by R. Penney.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0589131-1
PII: S 0002-9939(1981)0589131-1
Keywords: Rationally varying polarizing subalgebras, nilpotent Lie algebras, canonical subalgebras
Article copyright: © Copyright 1981 American Mathematical Society