C^n中单位球的双全纯与半交叉积
Biholomorphisms of the unit ball of C^n and semicrossed products
摘要：
假设$ϕ_1$和$ϕ_2$是非交换圆盘代数$\fA_n$，$n \geq 2$的自同构。证明了半交叉积$\fA_n \times_{ϕ_1} \bZ^+$和$\fA_n \times_{ϕ_2} \bZ^+$是代数同构的充要条件是$ϕ_1$和$ϕ_2$通过$\fA_n$的自同构共轭.对于d-移位代数$\A_d$，$d \geq 2$的半交叉积也有类似的结果.
英文摘要：
Assume that $ϕ_1$ and $ϕ_2$ are automorphisms of the non-commutative disc algebra $\fA_n$, $n \geq 2$. We show that the semicrossed products $\fA_n \times_{ϕ_1} \bZ^+$ and $\fA_n \times_{ϕ_2} \bZ^+$ are isomorphic as algebras if and only if $ϕ_1$ and $ϕ_2$ are conjugate via an automorphism of $\fA_n$. A similar result holds for semicrossed products of the d-shift algebra $\A_d$, $d \geq 2$.
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