Essential dimension of involutions and subalgebras
Essential dimension of involutions and subalgebras
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对合和子代数的基本维数
DOI：
10.1007/s11856-012-0037-9
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发表时间：
2012
影响因子：
1
通讯作者：
R. Lötscher
中科院分区：
文献类型：
--
作者：
R. Lötscher
本质维是代数群G在域F上的一个不变量，它度量了F的域扩张上G-扭矩的复杂性.利用N·Karpenko关于Severi-Brauer簇的不可压缩性和Severi-Brauer簇的二次Weil变换的定理，计算了RK/F(GL1(A))的某些闭子群的本质维，其中A是素数次幂中心除K-代数，K/F是≤次可分的域扩张.特别地，我们确定了(A，σ)的相似群Sim(A，σ)的本质维，其中σ是A上的F-对合，正规化子$$N_{GL_1(A)}\Left({GL_1\Left(B\Right)}\Right)$$的本质维度，其中B是A的可分子代数。
Essential dimension is an invariant of algebraic groups G over a field F that measures the complexity of G-torsors over field extensions of F. We use theorems of N. Karpenko about the incompressibility of Severi-Brauer varieties and quadratic Weil transfers of Severi-Brauer varieties to compute the essential dimension of some closed subgroups of RK/F (GL1(A)), where A is a central division K-algebra of prime power degree and K/F is a separable field extension of degree ≤ 2. In particular, we determine the essential dimension of the group Sim(A, σ) of similitudes of (A, σ), where σ is an F-involution on A, and the essential dimension of the normalizer $$N_{GL_1 (A)} \left( {GL_1 \left( B \right)} \right)$$, where B is a separable subalgebra of A.