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Transactions of the American Mathematical Society
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
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0304564-5
PII: S 0002-9947(1972)0304564-5
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