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arXiv · 2608.01036

Permutation of edges in mutation reduction of pointed Brauer trees

Reut Frenkel-Mayzlish·Mary Schaps·Zehavit Zvi
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Abstract

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.

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Reut Frenkel-Mayzlish, Mary Schaps, Zehavit Zvi. 2026-08-02. Permutation of edges in mutation reduction of pointed Brauer trees. https://arxiv.org/abs/2608.01036

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