论文标题
非语言Bernoulli动作的边界和刚性
Boundary and rigidity of nonsingular Bernoulli actions
论文作者
论文摘要
令$ g $为一个可计数的离散组，并考虑一个非介绍的bernoulli shift action $ g \ curvearrowrowrowright \ prod_ {g \ in g}（\ {0,1 \}，μ_g），μ_g）$，带有两个基点。如果$ g $确切，则在$ \ {μ_g\} _ {g \ in G} $的一定有限假设下，我们为Bernoulli交叉产品C $^*$ - 代数构建了一个边界，该界限承认在Ozawa的Bi-extactsical的意义上承认有些可承认和不舒服。结果，我们得到任何此类伯努利的行动都是牢固的。这概括了衡量衡量的稳固性，以保留Ozawa和Chifan（OioAana）的Bernoulli行动，这是不保留案例的第一个刚性结果。为了证明，我们使用反对称的Fock空间和左创建算子来构建边界，因此具有两个基点的假设至关重要。
Let $ G $ be a countable discrete group and consider a nonsingular Bernoulli shift action $ G \curvearrowright \prod_{g\in G }(\{0,1\},μ_g)$ with two base points. When $ G $ is exact, under a certain finiteness assumption on the measures $\{μ_g\}_{g\in G }$, we construct a boundary for the Bernoulli crossed product C$^*$-algebra that admits some commutativity and amenability in the sense of Ozawa's bi-exactness. As a consequence, we obtain that any such Bernoulli action is solid. This generalizes solidity of measure preserving Bernoulli actions by Ozawa and Chifan--Ioana, and is the first rigidity result in the non measure preserving case. For the proof, we use anti-symmetric Fock spaces and left creation operators to construct the boundary and therefore the assumption of having two base points is crucial.
