AI 中文总结
本文针对带点Brauer树的突变归约，定义带点广义Aihara算法并证明其置换为恒等，给出Kozakai算法置换的一般形式并举例说明。
AI 中文摘要
Aihara开发了一种针对Brauer树代数的算法，我们称之为突变归约，该算法通过一系列以边为中心的突变，将Brauer树代数转化为更简单的Brauer星代数。Schaps和Zvi利用Schaps-Zakay的树带点理论证明，不同的突变序列算法会产生边的置换。Kozakai提出了一种依赖于给定带点的突变归约新算法，并描述了带点在突变归约下的演化。本文中，我们定义了带点广义Aihara算法，并证明其置换为恒等置换；给出了Kozakai算法所得置换的一般形式，并以单分支二叉树的例子进行说明。
英文摘要
Aihara developed an algorithm for Brauer tree algebras, which we call a mutation reduction, for getting from a Brauer tree algebra to the simpler Brauer star algebra using a sequence of mutations centered on edges. Schaps and Zvi, using the Schaps-Zakay theory of pointing the tree, showed that different algorithms for the sequence of mutations give permutations of the edges. Kozakai gave a new algorithm for a mutation reduction that depends on a given pointing and describes the evolution of the pointing under the mutation reduction. In this paper, we define a pointed generalized Aihara algorithm and show that its permutation is the identity. We give a general form for the permutations resulting from Kozakai's algorithm, which we illustrate with examples from uni-branch binary trees.
