论文标题
准不变性状态
Quasi-invariant states
论文作者
论文摘要
我们在$*$ - $*$ - $*$ - 代数（或von neumann alegbra）$ g $的$ g $的行动下发展了准式（分别是quasi- invariant）的理论。我们证明，这些状态自然与左 - $ g $ - $ 1 $ - Cocycles相关。如果$ g $是紧凑的，则确定强烈的$ g $ - quasi-invariant状态的结构。对于任何$ g $ - 强烈的quasi - invariant状态$φ$，我们构建了与三重$（\ Mathcal {a}，g，φ）$相关的统一表示。 We prove, under some conditions, that any quantum Markov chain with commuting, invertible and hermitean conditional density amplitudes on a countable tensor product of type I factors is strongly quasi--invariant with respect to the natural action of the group $\mathcal{S}_{\infty}$ of local permutations and we give the explicit form of the associated cocycle.这为局部紧凑型组的非平地示例提供了一个非平整示例，这些属于局部紧凑的群体，这些群体是紧凑型组序列增加的电感限制。
We develop the theory of quasi--invariant (resp. strongly quasi--invariant) states under the action of a group $G$ of normal $*$--automorphisms of a $*$--algebra (or von Neumann alegbra) $\mathcal{A}$. We prove that these states are naturally associated to left--$G$--$1$--cocycles. If $G$ is compact, the structure of strongly $G$--quasi--invariant states is determined. For any $G$--strongly quasi--invariant state $φ$, we construct a unitary representation associated to the triple $(\mathcal{A},G,φ)$. We prove, under some conditions, that any quantum Markov chain with commuting, invertible and hermitean conditional density amplitudes on a countable tensor product of type I factors is strongly quasi--invariant with respect to the natural action of the group $\mathcal{S}_{\infty}$ of local permutations and we give the explicit form of the associated cocycle. This provides a family of non--trivial examples of strongly quasi--invariant states for locally compact groups obtained as inductive limit of an increasing sequence of compact groups.
