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

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

2011-11-10

arxiv.org/abs/1111.2387v2

Mathematics

Representation Theory

33 Pages; Made a minor change to Lemma 3.11 and its proof, and re-formulated Theorem 8.4

Scientific paper

Over an arbitrary field of characteristic $\ne 2$, 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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