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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differential forms on quotients by reductive group actions
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by Michel Brion PDF
Proc. Amer. Math. Soc. 126 (1998), 2535-2539 Request permission

Abstract:

Let $X$ be a smooth affine algebraic variety where a reductive algebraic group $G$ acts with a smooth quotient space $Y=X//G$. We show that the algebraic differential forms on $X$ which are pull-backs of forms on $Y$ are exactly the $G$-invariant horizontal differential forms on $X$.
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Additional Information
  • Michel Brion
  • Affiliation: Institut Fourier, B. P. 74, 38402 Saint-Martin d’Hères Cedex, France
  • MR Author ID: 41725
  • Email: mbrion@fourier.ujf-grenoble.fr
  • Received by editor(s): October 25, 1996
  • Received by editor(s) in revised form: January 29, 1997
  • Communicated by: Roe Goodman
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2535-2539
  • MSC (1991): Primary 14L30, 22E99
  • DOI: https://doi.org/10.1090/S0002-9939-98-04320-2
  • MathSciNet review: 1451789