Mutations and pointing for brauer tree algebras

Zehavit Zvi, Mary Schaps

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Brauer tree algebras are important and fundamental blocks in the representation theory of finite dimensional algebras. In this research, we present a combination of two main approaches to the tilting theory of Brauer tree algebras. The first approach is the theory initiated by Rickard, providing a direct link between an ordinary Brauer tree algebra and the Brauer star algebra. This approach was continued by Schaps-Zakay with their theory of pointing the tree. The second approach is the theory developed by Aihara, relating to the sequence of mutations from the ordinary Brauer tree algebra to the Brauer star algebra. Our main purpose in this research is to combine these two approaches. We first find an algorithm based on centers which are all terminal edges, for which we are able to obtain a tilting complex constructed from irreducible complexes of length two [13], which is obtained from a sequence of mutations. In [1], Aihara gave an algorithm for reducing from tree to star by mutations and showed that it gave a two-term tree-to-star complex. We prove that Aihara’s complex is obtained from the corresponding completely folded Rickard tree-to-star complex by a permutation of projectives.

Original languageEnglish
Pages (from-to)689-709
Number of pages21
JournalOsaka Journal of Mathematics
Issue number3
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020, Osaka University. All rights reserved.


Dive into the research topics of 'Mutations and pointing for brauer tree algebras'. Together they form a unique fingerprint.

Cite this