Group representable relation algebras play an important role in the study of representable relation algebras. The class of distributive involutive FL-algebras (DInFL-algebras) generalises relation algebras, as well as Sugihara monoids and MV-algebras. We construct DInFL-algebras from pregroups and show that they can be represented as algebras of binary relations. Even for finite pregroups we obtain relational representations of DInFL-algebras with non-Boolean lattice reducts. If the pregroup is enriched with a particular unary order-reversing operation, then our construction yields representation results for distributive quasi relation algebras.

翻译：群可表示关系代数在可表示关系代数的研究中扮演着重要角色。分配对合FL-代数类（DInFL-代数）推广了关系代数，同时也推广了杉原幺半群与MV-代数。我们从预群出发构造DInFL-代数，并证明它们可以表示为二元关系代数。即使对于有限预群，我们也能获得具有非布尔格约化结构的DInFL-代数的关系表示。若在预群中增添一个特定的单序逆序运算，则我们的构造将产生分配拟关系代数的表示结果。