Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Mutation of Brauer configuration algebras

Toshitaka Aoki, Yingying Zhang

Abstract

For Brauer graph algebras, tilting mutation is compatible with flip of Brauer graphs. The aim of this paper is to generalize this result to the class of Brauer configuration algebras introduced by Green and Schroll recently. More precisely, under a certain condition, we introduce flip of Brauer configurations and prove that it is compatible with tilting mutation of the corresponding Brauer configuration algebras.

Mutation of Brauer configuration algebras

Abstract

For Brauer graph algebras, tilting mutation is compatible with flip of Brauer graphs. The aim of this paper is to generalize this result to the class of Brauer configuration algebras introduced by Green and Schroll recently. More precisely, under a certain condition, we introduce flip of Brauer configurations and prove that it is compatible with tilting mutation of the corresponding Brauer configuration algebras.
Paper Structure (7 sections, 6 theorems, 9 equations, 1 figure, 1 table)

This paper contains 7 sections, 6 theorems, 9 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Tilting theory
  4. Brauer configurations
  5. Brauer configuration algebras
  6. Flip of Brauer configurations and main result
  7. Definition of flip

Key Result

Theorem 1.1

Tilting mutation of Brauer graph algebras is compatible with flip of Brauer graphs.

Figures (1)

  • Figure 1: Flip at a $5$-gon $V$ in the left and a (self-folded) $4$-gon $U$ in the right.

Theorems & Definitions (21)

  • Theorem 1.1: Aihara15, see also Kauer98
  • Proposition 1.2: Example \ref{['example:BCAtilting']}
  • Definition 1.3: See Definitions \ref{['def:conditionE']} and \ref{['def:flip BC']} for the details
  • Theorem 1.4: Theorem \ref{['thm:main theorem']}
  • Definition 2.1
  • Theorem 2.2
  • Example 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.8
  • ...and 11 more