Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1981-0589131-1
MathSciNet review: 589131
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17B30

Retrieve articles in all journals with MSC: 17B30


Additional Information

Keywords: Rationally varying polarizing subalgebras, nilpotent Lie algebras, canonical subalgebras
Article copyright: © Copyright 1981 American Mathematical Society