Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T00:44:26.551Z Has data issue: false hasContentIssue false
  • English
  • Français

Cohomology Theorems for Borel-Like Solvable Lie Algebras in Arbitrary Characteristic

Published online by Cambridge University Press:  20 November 2018

G. Leger  and
E. Luks
G. Leger
Affiliation:
Tufts University, Medford, Massachusetts
E. Luks
Affiliation:
Bucknell University, Lewisburg, Pennsylvania
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper develops some techniques for the study of derivation algebras and cohomology groups of Lie algebras. We are especially concerned with solvable algebras over arbitrary fields with structural properties like those of the Borel subalgebras of complex semi-simple Lie algebras. In particular, these algebras are semi-direct sums of nilpotent ideals and abelian subalgebras which act on the ideals in a semi-simple fashion. We make strong use, in our discussion, of a cohomology theorem of Hochschild-Serre. This result is stated herein (§ 2) in a modified form which allows us to omit the original hypothesis that the base field have characteristic 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1019 - 1026
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Hochschild, G. and Serre, J.-P., Cohomology of Lie algebras, Ann. of Math. 57 (1953), 591–603.Google Scholar
2. Jacobson, N., Lie algebras (Interscience, New York, 1962).Google Scholar
3. Kostant, B., Lie algebra cohomology and generalized Schubert cells, Ann. of Math. 77 (1963), 72–144.Google Scholar
4. Leger, G. and Luks, E., Lie algebras and trees (to appear).Google Scholar
5. Nijenhuis, A. and Richardson, R., Deformations of Lie algebra structures, J. Math. Mech. 17 (1967), 89–105.Google Scholar
6. Richardson, R., On the rigidity of semi-direct products of Lie algebras, Pacific J. Math. 22 (1967), 339–344.Google Scholar
7. Tôgô, S., On some properties of t(n, Φ) and st(n, Φ), J. Sci. Hiroshima Univ. Sec. A-l Math. 31 (1967), 35–58.Google Scholar