量子B-modules

Pub Date : 2022-02-15 DOI:10.1002/malq.202100029

Xia Zhang, Wolfgang Rump

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引用次数: 1

摘要

量子b代数是描述量子的剩余结构的部分有序代数。例子出现在代数逻辑、非交换算术和量子理论中。具有平凡偏序的量子b代数等价于一个群。本文介绍了一种相应的量子模的模拟。证明了每个量子b模都有一个单射包络，该包络是一个量子模。注入包络被明确地构造为一个补全，一个Dedekind和MacNeille补全的多偏序集版本。

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Quantum B-modules

Quantum B-algebras are partially ordered algebras characterizing the residuated structure of a quantale. Examples arise in algebraic logic, non-commutative arithmetic, and quantum theory. A quantum B-algebra with trivial partial order is equivalent to a group. The paper introduces a corresponding analogue of quantale modules. It is proved that every quantum B-module admits an injective envelope which is a quantale module. The injective envelope is constructed explicitly as a completion, a multi-poset version of the completion of Dedekind and MacNeille.

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