紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2020, 57(3), p. 689-709

MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2020-07

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.

10.18910/76681

76681

MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS

Osaka University and Osaka City University, Departments of Mathematics

英語

2020-07

Osaka Journal of Mathematics

57

3

689

709

https://hdl.handle.net/11094/76681

10.18910/76681

https://doi.org/10.18910/76681