论文标题
代数群作为代数的自动形态群体
Algebraic groups as automorphism groups of algebras
论文作者
论文摘要
我们表明，在具有至少8个元素的字段上的每个代数组方案都可以实现为非缔约代数的自动形态。这只是Gordeev和Popov（2003）定理的一个适度改进，但它使我们能够对代数Lie代数的新表征进行新的表征，并简化Mumford-Tate域和Shimura品种的标准描述为模仿空间。一旦Gordeev和Popov的原始论点用计划的语言重写，我们发现它也适用于离散估值环的代数群体。
We show that every algebraic group scheme over a field with at least 8 elements can be realized as the group of automorphisms of a nonassociative algebra. This is only a modest improvement of the theorem of Gordeev and Popov (2003), but it allows us to give a new characterization of algebraic Lie algebras and to simplify the standard descriptions of Mumford--Tate domains and Shimura varieties as moduli spaces. Once the original argument of Gordeev and Popov has been rewritten in the language of schemes, we find that it also applies to algebraic groups over discrete valuation rings.
