Invariant polynomials on Lie algebras of inhomogeneous unitary and special orthogonal groups
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- by S. J. Takiff
- Trans. Amer. Math. Soc. 170 (1972), 221-230
- DOI: https://doi.org/10.1090/S0002-9947-1972-0304564-5
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Abstract:
The ring of invariant polynomials for the adjoint action of a Lie group on its Lie algebra is described for the inhomogeneous unitary and special orthogonal groups. In particular a new proof is given for the fact that this ring for the inhomogeneous Lorentz group is generated by two algebraically independent homogeneous polynomials of degrees two and four.References
- Claude Chevalley, Theory of Lie groups. I, Princeton University Press, Princeton, N. J., 1946 1957. MR 0082628
- B. Gruber and L. Oā€™Raifeartaigh, $S$ theorem and construction of the invariants of the semisimple compact Lie algebras, J. Mathematical Phys. 5 (1964), 1796ā€“1804. MR 169952, DOI 10.1063/1.1704102
- SigurÄ‘ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455 L. Oā€™Raifeartaigh, Lectures on local Lie groups and their representations, The Institute of Mathematical Sciences, Madras, 1964.
- Joe Rosen, Construction of invariants for Lie algebras of inhomogeneous pseudo-orthogonal and pseudo-unitary groups, J. Mathematical Phys. 9 (1968), 1305ā€“1307. MR 231949, DOI 10.1063/1.1664714
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 170 (1972), 221-230
- MSC: Primary 22E60
- DOI: https://doi.org/10.1090/S0002-9947-1972-0304564-5
- MathSciNet review: 0304564