Affine algebraic super-groups with integral
Affine algebraic super-groups with integral
复制标题
具有积分的仿射代数超群
DOI：
10.1080/00927872.2021.1963758
复制
发表时间：
2021
影响因子：
0.7
通讯作者：
Shimada Yuta
中科院分区：
文献类型：
--
作者：
Masuoka Akira;Shibata Taiki;Shimada Yuta
我们将一个已知的事实推广到超上下文，即：如果在交换环上的仿射代数群在仿射模式˜˜上自由地(在适当的意义下)作用，则G-轨道的Dur Sheaf X/Xoverk G在以下两种情况下是仿射格式：(I)G是有限的；(Ii)k是域，G是线性约化的。重点讨论了第二种情况下更难的推广，取而代之的假设是任意域上的仿射代数超群有一个积分。利用包括玻色化在内的Hopf-代数技巧，刻画了满足这一假设的超群，并发现它们构成了一大类超群。
We generalize to the super context, the known fact that if an affine algebraic groupGover a commutative ringkacts freely (in an appropriate sense) on an affine schemeXoverk, then the dur sheaf X/˜˜G ofG-orbits is an affine scheme in the following two cases: (I)Gis finite; (II)kis a field, andGis 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-groupGover an arbitrary field has an integral. Those super-groups which satisfy the assumption are characterized, and are seen to form a large class ifHopf-algebraic techniques including bosonization are applied to prove the results.