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The scheme of Lie sub-algebras of a Lie algebra and the equivariant cotangent map*

Published online by Cambridge University Press:  22 January 2016

William J. Haboush
William J. Haboush*
Affiliation:
Nagoya University and The State University of New York
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The main object of this paper is to develop techniques for investigating the local properties of actions of an algebraic group on an algebraic variety. Our main tools are certain schemes which may be associated to Lie algebras.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 53 , May 1974 , pp. 59 - 70
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

Footnotes

*

Part of this research (sections 1 and 2) was supported by a New York State research grant. The greater part of it, however, was made possible by the generous support of the Japan Society for the Promotion of Science.

References

[1] Borel, A.: Linear Algebraic Groups (Notes by Bass, H.) W. A. Benjamin, Inc. New York 1969.Google Scholar
[2] Borel, A. et al.: Seminar on Transformation Groups, Annals of Mathematics Studies, Number 46, Princeton University Press, Princeton New Jersey 1960.Google Scholar
[3] Mumford, D.: Abelian Varieties, Published for The Tata Institute of Fundamental Research, Bombay, Oxford University Press, Bombay India, 1970.Google Scholar
[4] Richardson, R. W.: Principal Orbit Types for Algebraic Transformation Spaces in Characteristic Zero, Inventiones Math., 16, 6-14, 1972, pp. 7–14.Google Scholar
[5] Haboush, W. J.: Deformation Theoretic Methods in the Theory of Algebraic Transformation Spaces, Kyoto Journal of Mathematics, To appear.Google Scholar