完备原子格的弱张量积
Weak tensor products of complete atomistic lattices
摘要：
给定两个完备原子格L_1和L_2，利用三个公理（对于描述分离的量子复合系统是自然的），或利用关于给定的一类双态的泛性质，定义完备原子格的集合S（L_1，L_2）.我们称S（L_1，L_2）中的元素为L_1和L_2的弱张量积。我们证明了S（L_1，L_2）是一个完全格.我们比较底部元素与分离的产品的Aesthetz和盒产品的Graetzer和Wehrung。同样，我们比较了顶元素与Fraser，Chu和Shmuely的张量积。在对L_1和L_2作了一些附加的假设（例如L_1和L_2是不可约的、正交可补的和具有覆盖性质的）后，我们用L_1和L_2的自同构刻画了弱张量积的自同构。
英文摘要：
Given two complete atomistic lattices L_1 and L_2, we define a set S(L_1,L_2) of complete atomistic lattices by means of three axioms (natural regarding the description of separated quantum compound systems), or in terms of a universal property with respect to a given class of bimorphisms. We call the elements of S(L_1,L_2) weak tensor products of L_1 and L_2. We prove that S(L_1,L_2) is a complete lattice. We compare the bottom element with the separated product of Aerts and with the box product of Graetzer and Wehrung. Similarly, we compare the top element with the tensor products of Fraser, Chu and Shmuely. With some additional hypotheses on L_1 and L_2 (true for instance if L_1 and L_2 are moreover irreducible, orthocomplemented and with the covering property), we characterize the automorphisms of weak tensor products in terms of those of L_1 and L_2.
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