Permutation of edges in mutation reduction of pointed Brauer trees

Reut Frenkel-Mayzlish; Mary Schaps; Zehavit Zvi

Permutation of edges in mutation reduction of pointed Brauer trees

Combinatorics 2026-08-02 v1 Representation Theory

Authors: Reut Frenkel-Mayzlish , Mary Schaps , Zehavit Zvi

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.

Keywords

Brauer tree algebras mutation reduction pointed trees permutations Aihara algorithm

Cite

@article{arxiv.2608.01036,
  title  = {Permutation of edges in mutation reduction of pointed Brauer trees},
  author = {Reut Frenkel-Mayzlish and Mary Schaps and Zehavit Zvi},
  journal= {arXiv preprint arXiv:2608.01036},
  year   = {2026}
}