论文标题
Clifford系统扩展的实现 - 目标精确序列
Realization-obstruction exact sequences for Clifford system extensions
论文作者
论文摘要
对于每一个动作$ ϕ \ in \ text {hom}（g，\ text {aut} _k（k））$的$ g $在交换戒指上$ k $，我们介绍了两个abelian monoids。 monoid $ \ text {cliff} _k（ϕ）$由$ g $的clifford系统扩展为$ k $ k $ g $ central代数的等效类。 MONOID $ \ MATHCAL {C} _K {（ϕ）} $由类型$ G $的类型$ G $的普通集体字符组成，到$ k $ central代数的Picard组。此外，对于每一个这样的$ ϕ $，都有一个确切的Abelian单体$$ 0 \ to H^2（g，k^*_ϕ）\ to \ text {cliff} _k（ϕ）\ to \ nathcal {c} _k} _k} _k {（（（（c}））过滤，终止上述序列。当$ ϕ $是GALOIS动作时，Brauer组的限制性攻击序列是该序列的确切次级单子序列的图像。
For every action $ϕ\in\text{Hom}(G,\text{Aut}_k(K))$ of a group $G$ on a commutative ring $K$ we introduce two abelian monoids. The monoid $\text{Cliff}_k(ϕ)$ consists of equivalent classes of $G$-graded Clifford system extensions of type $ϕ$ of $K$-central algebras. The monoid $\mathcal{C}_k{(ϕ)}$ consists of equivariant classes of generalized collective characters of type $ϕ$ from $G$ to the Picard groups of $K$-central algebras. Furthermore, for every such $ϕ$ there is an exact sequence of abelian monoids $$0\to H^2(G,K^*_ϕ)\to\text{Cliff}_k(ϕ)\to\mathcal{C}_k{(ϕ)}\to H^3(G,K^*_ϕ).$$ The rightmost homomorphism is often surjective, terminating the above sequence. When $ϕ$ is a Galois action, then the restriction-obstruction sequence of Brauer groups is an image of an exact sequence of sub-monoids of this sequence.
