From Brauer graph algebras to biserial weighted surface algebras

2017/06/22 by Karin Erdmann, Erdmann, Karin, Andrzej Skowroński +1
Mathematics · #05E99 #16G20 #16G70 #20C20 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E99 #msc:16G20 #msc:16G70 #msc:20C20

paper · pdf · doi:10.48550/arxiv.1706.07693

arXiv admin note: text overlap with arXiv:1706.00688 and arXiv:1703.02346

arxiv created 2018/08/22 · arxiv updated 2018/08/23

Abstract

We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These algebras are associated to triangulated surfaces with arbitrarily oriented triangles, investigated in [17] and [18]. Moreover we prove that Brauer graph algebras are idempotent algebras of periodic weighted surface algebras, investigated in [17] and [19].

Citations

• Weighted Surface Algebras

Related

• Brauer graph algebras
• Trivial Extensions of Gentle Algebras and Brauer Graph Algebras
• Skew-Brauer graph algebras
• Quasi-biserial algebras, special quasi-biserial algebras and symmetric fractional Brauer graph algebras
• Weighted surface algebras: general version