We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the atom structures used to study relation algebras. We also extend the duality from complete perfect algebras to all algebras, using so-called doubly-pointed frames with a Priestley topology. We then turn to the representability of these algebras as lattices of binary relations. Some algebras can be realised as term subreducts of representable relation algebras and are hence representable. We provide a detailed account of known representations for all algebras up to size six.

翻译：本文为完备完美分配拟关系代数与完备完美分配对合FL-代数建立了对偶理论。其对偶对象是带有附加结构的偏序框架。这些框架类似于研究关系代数时使用的原子结构。我们进一步利用具有Priestley拓扑的双点框架，将对偶理论从完备完美代数推广至所有代数。随后，我们探讨了这些代数作为二元关系格的表示性问题。部分代数可实现为可表示关系代数的项子约化代数，因而具有可表示性。我们对所有六元及以下代数的已知表示给出了系统阐述。