We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids indicate that they should give origin to new knot algebras; indeed, our tied monoids include the tied braid monoid and the tied singular braid monoid, which were used, respectively, to construct new polynomial invariants for classical links and singular links. Consequently, we provide a mechanism to attach an algebra to each tied monoid; this mechanism not only captures known generalizations of the bt-algebra, but also produces possible new knot algebras. To build the tied monoids it is necessary to have presentations of set partition monoids of types A, B and D, among others. For type A we use a presentation due to FitzGerald and for the other type it was necessary to built them.

我们构造了某些幺半群，称为绑定幺半群. 这些幺半群的结果是有限呈现的半直积，并且通常由辫子群及其作用在集合分区的幺半群上的亲戚构建。我们幺半群的性质表明它们应该是新结代数的起源；事实上，我们的束缚幺半群包括束缚编织幺半群和束缚奇异编织幺半群，它们分别用于为经典链接和奇异链接构建新的多项式不变量。因此，我们提供了一种将代数附加到每个绑定幺半群的机制；这种机制不仅捕获了 bt 代数的已知概括，而且还产生了可能的新结代数。要构建绑定幺半群，有必要展示 A、B 和 D 类型的集合分割幺半群，等等。对于A型 我们使用了 FitzGerald 的演示文稿，而对于另一种类型，则需要构建它们。