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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Invariant polynomials on Lie algebras of inhomogeneous unitary and special orthogonal groups
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by S. J. Takiff PDF
Trans. Amer. Math. Soc. 170 (1972), 221-230 Request permission

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
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Additional 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