PlanetMath: invariant polynomial

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invariant polynomial

(Definition)

An invariant polynomial is a polynomial that is invariant under a (compact) Lie group $\Gamma$ acting on a vector space . Therefore is $\Gamma$ -invariant polynomial if $P(\gamma x) = P(x)$ for all $\gamma \in \Gamma$ and $x \in V$ .

Bibliography

GSS: Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.

"invariant polynomial" is owned by Daume.

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Cross-references: vector space, Lie group, compact, invariant, polynomial
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This is version 3 of invariant polynomial, born on 2003-06-10, modified 2007-06-10.
Object id is 4337, canonical name is InvariantPolynomial.
Accessed 2303 times total.

Classification:

AMS MSC:

13A50 (Commutative rings and algebras :: General commutative ring theory :: Actions of groups on commutative rings; invariant theory)

Pending Errata and Addenda

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