论文标题
在平面表面的绞线代数上
On skein algebras of planar surfaces
论文作者
论文摘要
令$ r $为具有身份的交换戒指和固定的可逆元素$ q^{\ frac {1} {2}} $。令$ \ Mathcal {s} _n $表示平面表面$σ_{0，n+1} $上$ r $的Kauffman支架skein代数。当$ q+q^{ - 1} $在$ r $中可逆时，我们找到了$ \ nathcal {s} _n $的生成集，并证明定义关系的理想是由学位的最多6 $支撑的$ 6 $支持的$ 6 $支撑的$ 6 $ andermorphics支持的$ 6 $ n hos and hosermorphic to $σ_{0，k+1，k+1} $ k $ 6 $ 6。当$ q+q^{ - 1} $不可逆转时，我们找到了另一个用于$ \ Mathcal {s} _n $的生成集，并证明定义关系的理想是由某些学位关系最多以$ 2N+2 $而生成的。
Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$. Let $\mathcal{S}_n$ denote the Kauffman bracket skein algebra of the planar surface $Σ_{0,n+1}$ over $R$. When $q+q^{-1}$ is invertible in $R$, we find a generating set for $\mathcal{S}_n$, and show that the ideal of defining relations is generated by relations of degree at most $6$ supported by certain subsurfaces homeomorphic to $Σ_{0,k+1}$ with $k\le 6$. When $q+q^{-1}$ is not invertible, we find another generating set for $\mathcal{S}_n$, and show that the ideal of defining relations is generated by certain relations of degree at most $2n+2$.
