论文标题
具有积分不可或缺的代数超级组
Affine algebraic super-groups with integral
论文作者
论文摘要
我们概括了超级上下文，即已知的事实，即如果在$ k $上的仿射方案$ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x \ x \ x \ tilde {\ tilde {\ tilde {/} g $ g $ g $ g $ iS at aft tw twos and caster and castection castection $ g $ g $ iS ADRECHS and conter tw off casection，则是aft tw tw tus two and， （ii）$ k $是一个字段，$ g $是线性还原的。在第二种情况下，强调的是更加困难的概括。然后，替换的假设是，在任意字段上，仿射代数超级$ g $具有积分。那些满足假设的超级组的表征，如果$ \ operatatorName {char} k = 0 $，则会形成大型类。 HOPF代数技术（包括氯化）用于证明结果。
We generalize to the super context, the known fact that if an affine algebraic group $G$ over a commutative ring $k$ acts freely (in an appropriate sense) 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, 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.
