广义四元数群代数的可分离变形
Separable deformations of the generalized quaternion group algebras
摘要：
将域$k$上包含$\mathbb{F}_{2^{n-2}}$的广义四元数群$Q_{2^n}$的群代数$kQ_{2^n}$变形为可分$k((t))$ -代数$[kQ_{2^n}]_t$ .代数闭包$\overline{k((t))}$上的$\overline{k((t))}\otimes_{k((t))}[kQ_{2^n}]_t$和$\mathbb {C}$上的$\mathbb{C} Q_{2^n}$的简单分支的维数是相同的，从而得到了广义四元数群的Donald-Flanigan猜想的强解。
英文摘要：
The group algebras $kQ_{2^n}$ of the generalized quaternion groups $Q_{2^n}$ over fields $k$ which contain $\mathbb{F}_{2^{n-2}}$, are deformed to separable $k((t))$-algebras $[kQ_{2^n}]_t$. The dimensions of the simple components of $\overline{k((t))}\otimes_{k((t))}[kQ_{2^n}]_t$ over the algebraic closure $\overline{k((t))}$, and those of $\mathbb{C} Q_{2^n}$ over $\mathbb {C}$ are the same, yielding strong solutions of the Donald-Flanigan conjecture for the generalized quaternion groups.
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