Linearizing certain reductive group actions

H. Bass; W. Haboush

doi:10.1090/S0002-9947-1985-0808732-4

Linearizing certain reductive group actions

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Abstract

Is every algebraic action of a reductive algebraic group G on affine space Cⁿ equivalent to a linear action? The “normal linearization theorem” proved below implies that, if each closed orbit of G is a fixed point, then Cⁿ is G-equivariantly isomorphic to (Cⁿ)^G X C^m for some linear action of G on Cm.

Original language	English (US)
Pages (from-to)	463-482
Number of pages	20
Journal	Transactions of the American Mathematical Society
Volume	292
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1985-0808732-4
State	Published - Dec 1985
Externally published	Yes

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Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1985-0808732-4

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abstract = "Is every algebraic action of a reductive algebraic group G on affine space Cn equivalent to a linear action? The “normal linearization theorem” proved below implies that, if each closed orbit of G is a fixed point, then Cn is G-equivariantly isomorphic to (Cn)G X Cm for some linear action of G on Cm.",

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Linearizing certain reductive group actions

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