MISC

2020年3月11日

Affine algebraic super-groups with integral

  • Akira Masuoka
  • ,
  • Taiki Shibata
  • ,
  • Yuta Shimada

We generalize to the super context, the known fact that if an affine
algebraic group $G$ over a commutative ring $k$ acts freely on an affine scheme
$X$ over $k$, then the dur sheaf $X\tilde{\tilde{/ } }G$ of $G$-orbits is an
affine scheme in the following two cases: (I) $G$ is finite; (II) $k$ is a
field of characteristic zero, and $G$ is linearly reductive. An emphasize is
put on the more difficult generalization in the second case; the replaced
assumption then is that an affine algebraic super-group $G$ over an arbitrary
field has an integral. Those super-groups which satisfy the assumption are
characterized, and are seen to form a large class if $\operatorname{char}k=0$.
Hopf-algebraic techniques including bosonization are applied to prove the
results.

リンク情報
arXiv
http://arxiv.org/abs/arXiv:2003.05100
Arxiv Url
http://arxiv.org/abs/2003.05100v2
Arxiv Url
http://arxiv.org/pdf/2003.05100v2 本文へのリンクあり
ID情報
  • arXiv ID : arXiv:2003.05100

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