论文标题
高级自由谎言代数的均匀性
Uniformity in Higher class Free Lie algebras
论文作者
论文摘要
令$ \ mathfrak {f} _ {c，2} $表示免费的class- $ c $ lie lies戒指$ 2 $生成器。我们研究了$ \ mathfrak {f} _ {c，2}（\ mathbb {f} _p）$ in $ c \ leq6 $中的ZETA函数，以$ c \ leq5 $ c $ c \ c \ leq5 $ c = $ c = $ c $ c = for $ c yous p $ cy n yous p $ cy n of p $ c。我们还表明，Zeta函数列举一步分级的理想$ \ mathfrak {f} _ {c，2}（\ Mathbb {f} _p）$始终由$ p $在所有$ c $的$ p $中给出。
Let $\mathfrak{f}_{c,2}$ denote a free class-$c$ Lie rings on $2$ generators. We investigate the zeta functions enumerating graded ideals in $\mathfrak{f}_{c,2}(\mathbb{F}_p)$ for $c\leq6$, prove that they are uniformly given by polynomials in $p$ for $c\leq5$ and not uniformly given by a polynomial in $p$ for $c=6$. We also show that the zeta functions enumerating one-step graded ideals $\mathfrak{f}_{c,2}(\mathbb{F}_p)$ is always given by a polynomial in $p$ for all $c$.
