Quantum triads: an algebraic approach

TL;DR

This paper introduces the concept of quantum triads, providing an algebraic framework that unifies various structures like quantales, operator algebras, and orthomodular lattices through bilinear inner products.

Contribution

It presents the novel concept of quantum triads and their solutions, offering a unified algebraic approach for multiple quantum structures.

Findings

Defines quantum triads and their solutions

Unifies various quantum algebraic structures

Provides examples including quantaloids and operator algebras

Abstract

A concept of quantum triad and its solution is introduced. It represents a common framework for several situations where we have a quantale with a right module and a left module, provided with a bilinear inner product. Examples include Van den Bossche quantaloids, quantum frames, simple and Galois quantales, operator algebras, or orthomodular lattices.