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Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field

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Abstract

Over an arbitrary field of characteristic ≠ 2, we define the notion of Harish-Chandra pairs, and prove that the category of those pairs is anti-equivalent to the category of algebraic affine supergroup schemes. The result is applied to characterize some classes of affine supergroup schemes such as those which are (a) simply connected, (b) unipotent or (c) linearly reductive in positive characteristic.

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  1. Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan

    Akira Masuoka

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  1. Akira Masuoka
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Correspondence to Akira Masuoka.

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Dedicated to Margaret Beattie in honor of her distinguished career

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Masuoka, A. Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field. Transformation Groups 17, 1085–1121 (2012). https://doi.org/10.1007/s00031-012-9203-8

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  • DOI: https://doi.org/10.1007/s00031-012-9203-8

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