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Transactions of the American Mathematical Society

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Linearizing certain reductive group actions


Authors: H. Bass and W. Haboush
Journal: Trans. Amer. Math. Soc. 292 (1985), 463-482
MSC: Primary 14L30; Secondary 20G05
DOI: https://doi.org/10.1090/S0002-9947-1985-0808732-4
MathSciNet review: 808732
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Abstract: Is every algebraic action of a reductive algebraic group $ G$ on affine space $ {{\mathbf{C}}^n}$ equivalent to a linear action? The "normal linearization theorem" proved below implies that, if each closed orbit of $ G$ is a fixed point, then $ {{\mathbf{C}}^n}$ is $ G$-equivariantly isomorphic to $ {({{\mathbf{C}}^n})^G} \times {{\mathbf{C}}^m}$ for some linear action of $ G$ on $ {{\mathbf{C}}^m}$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0808732-4
Article copyright: © Copyright 1985 American Mathematical Society

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