AI 中文总结
研究Brauer树代数的突变约简效率，对Aihara算法进行修改并测试计算效率，证明其在达到Brauer星所需步骤数最少方面是最快的，相比其他完全突变约简算法有优势。
AI 中文摘要
Brauer树代数是群的模表示理论中的重要基本块。Aihara开发了一种算法（我们称为突变约简），通过以边为中心的一系列突变从Brauer树代数得到更简单的Brauer星代数。Schaps和Zvi利用树指向的Schaps-Zakay理论表明，不同的突变序列算法会给出边的置换。我们对Aihara算法进行了修改，并针对原始算法测试了计算效率。我们证明，与所有可能的完全突变约简算法相比，Aihara算法的所有版本在达到Brauer星所需步骤数最少的意义上是最快的。
英文摘要
Brauer tree algebras are important and fundamental blocks in the modular representation theory of groups. Aihara develped an algorithm, 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. We give a modification of Aihara's algorithm and tested it against the original algorithm for computational efficiency. We prove that all versions of Aihara's algorithm are the fastest possible in the sense of requiring the least number steps to reach the Brauer star, when compared to all possible complete mutation reduction algorithms.
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