论文标题
切线配合物和钻石引理
Tangent complexes and the Diamond Lemma
论文作者
论文摘要
伯格曼（Bergman）著名的钻石引理提供了有效验证的标准，以正常形式的唯一性标准，用于在联想代数中的术语重写。我们提出了一种从同位代数的角度来解释和证明这一结果的新方法。我们的主要结果指出，具有单一关系的代数的每个多重自由分辨率都会引起其自身的钻石引理，因此伯格曼的“可分离歧义性”条件成为相应较连接的复合物中Maurer-Cartan方程的第一个非平凡分量。同样的方法适用于许多其他代数结构，强调了与单一关系计算代数的乘法自由分辨率的相关性。
The celebrated Diamond Lemma of Bergman gives an effectively verifiable criterion of uniqueness of normal forms for term rewriting in associative algebras. We present a new way to interpret and prove this result from the viewpoint of homotopical algebra. Our main result states that every multiplicative free resolution of an algebra with monomial relations gives rise to its own Diamond Lemma, so that Bergman's condition of "resolvable ambiguities" becomes the first non-trivial component of the Maurer--Cartan equation in the corresponding tangent complex. The same approach works for many other algebraic structures, emphasizing the relevance of computing multiplicative free resolutions of algebras with monomial relations.
