某些域上特殊和一般线性群的Reidemeister谱包含1
Reidemeister spectrum of special and general linear groups over some fields contains 1
摘要：
证明了若$\mathbb{F}$是一个零特征的代数闭域，且在$\mathbb{Q}$上具有无限超越度，则存在${\rm SL}_n(\mathbb{F})$和${\rm GL}_n(\mathbb{F})$的域自同构$φ$，使得$R(φ)=1$ .这一事实意味着${\rm SL}_n(\mathbb{F})$和${\rm GL}_n(\mathbb{F})$不具有$R_{\infty}$ -性质。然而，如果$\mathbb{F}$在$\mathbb{Q}$上的超越度是有限的，则已知${\rm SL}_n(\mathbb{F})$和${\rm GL}_n(\mathbb{F})$具有$R_{\infty}$ -性质。
英文摘要：
We prove that if $\mathbb{F}$ is an algebraically closed field of zero characteristic which has infinite transcendence degree over $\mathbb{Q}$, then there exists a field automorphism $φ$ of ${\rm SL}_n(\mathbb{F})$ and ${\rm GL}_n(\mathbb{F})$ such that $R(φ)=1$. This fact implies that ${\rm SL}_n(\mathbb{F})$ and ${\rm GL}_n(\mathbb{F})$ do not possess the $R_{\infty}$-property. However, if the transcendece degree of $\mathbb{F}$ over $\mathbb{Q}$ is finite, then ${\rm SL}_n(\mathbb{F})$ and ${\rm GL}_n(\mathbb{F})$ are known to possess the $R_{\infty}$-property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
