Abstract
If K is a compact semi-simple Lie group and g is the complexification of its Lie algebra then one knows that the algebra ? of (Maurer-Cartan) complex-valued left invariant differential forms may be naturally identified with the exterior algebra ?g. Also, one knows then that ?g is stable under the Laplacian defined with respect to the canonical Riemannian metric on K.
(Received 29 August 1963)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Borel: Groupes linéaires algébriques, Ann. Math., Princeton 64 (1956), 20–82.
B. Kostant: Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. Math, Princeton 74 (1961), 329–387.
J. L. Koszul: Homologie et cohomologie des algebres de Lie, Bull. Soc. Math. Fr. 78 (1950), 65–627.
A. I. Malcev: Commutative subalgebras of semi-simple Lie algebras, Izv. Akad. Nauk SSR, Ser. Mat. 9 (1945), 291–300 (Russian); Translation No. 40, Series 1, American Mathematical Society (English).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag New York
About this chapter
Cite this chapter
Kostant, B. (2009). Eigenvalues of a Laplacian and Commutative Lie Subalgebras. In: Joseph, A., Kumar, S., Vergne, M. (eds) Collected Papers. Springer, New York, NY. https://doi.org/10.1007/b94535_19
Download citation
DOI: https://doi.org/10.1007/b94535_19
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-09582-0
Online ISBN: 978-0-387-09583-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)