We study morphisms of the generalized quantum logic of tripotents in JBW\(^*\)-triples and von Neumann algebras. Especially, we establish a generalization of celebrated Dye’s theorem on orthoisomorphisms between von Neumann lattices to this new context. We show the existence of a one-to-one correspondence between the following maps: (1) quantum logic morphisms between the posets of tripotents preserving reflection \(u\rightarrow - u\) (2) maps between triples that preserve tripotents and are real linear on sets of elements with bounded range tripotents. In a more general description we show that quantum logic morphisms on structure of tripotents are given by a family of Jordan *-homomorphisms on Peirce 2-subspaces. By examples we demonstrate optimality of the results. Besides we show that the set of partial isometries with its partial order and orthogonality relation is a complete Jordan invariant for von Neumann algebras.

我们研究JBW \（^ * \）- triple和von Neumann代数中三能级广义量子逻辑的态射。尤其是，我们建立了关于冯·诺依曼格之间的同构同构的著名Dye定理的一个推广。我们显示出以下映射之间存在一一对应的关系：（1）三能子的波峰之间的量子逻辑态射保持反射\（u \ rightarrow-u \）（2）三元组之间的地图保留了三方性，并且在具有有限范围三方性的元素集上是线性的。在更笼统的描述中，我们表明，三重结构上的量子逻辑同态是由Peirce 2-子空间上的约旦*-同态族给出的。通过示例，我们证明了结果的最优性。此外，我们证明了具有部分顺序和正交关系的部分等距集是冯·诺依曼代数的一个完全乔丹不变量。