Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Invariant polynomials on Lie algebras of inhomogeneous unitary and special orthogonal groups

Author: S. J. Takiff
Journal: Trans. Amer. Math. Soc. 170 (1972), 221-230
MSC: Primary 22E60
MathSciNet review: 0304564
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] C. Chevalley, Theory of Lie groups. I, Princeton Math. Series, vol. 8, Princeton Univ. Press, Princeton, N.J., 1946. MR 7, 412. MR 0082628 (18:583c)
  • [2] B. Gruber and L. O'Raifeartaigh, $ S$ theorem and construction of the invariants of the semisimple compact Lie algebras, J. Mathematical Phys. 5 (1964), 1796-1804. MR 30 # 195. MR 0169952 (30:195)
  • [3] S. Helgason, Differential geometry and symmetric spaces, Pure and Appl. Math., vol. 12, Academic Press, New York, 1962. MR 26 #2986. MR 0145455 (26:2986)
  • [4] L. O'Raifeartaigh, Lectures on local Lie groups and their representations, The Institute of Mathematical Sciences, Madras, 1964.
  • [5] J. Rosen, Construction of invariants for Lie algebras of inhomogeneous pseudoorthogonal and pseudo-unitary groups, J. Mathematical Phys. 9 (1968), 1305-1307. MR 38 #275. MR 0231949 (38:275)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E60

Retrieve articles in all journals with MSC: 22E60

Additional Information

Keywords: Invariant polynomials, inhomogeneous unitary group, inhomogeneous special orthogonal group, inhomogeneous Lorentz group, adjoint representation, Zariski dense, algebraically independent polynomials, contragradient representation, complexification, real form
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society