Higher Tetrahedral Algebras

2017/06/13 by Karin Erdmann, Erdmann, Karin, Andrzej Skowro'nski +1 · 1 citation
Mathematics · #16D50 #16G20 #16G60 #16S80 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16D50 #msc:16G20 #msc:16G60 #msc:16S80

paper · pdf · doi:10.48550/arxiv.1706.04477

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

arxiv created 2017/11/27 · arxiv updated 2017/11/28

Abstract

We introduce and study the higher tetrahedral algebras, an exotic family of finite-dimensional tame symmetric algebras over an algebraically closed field. The Gabriel quiver of such an algebra is the triangulation quiver associated to the coherent orientation of the tetrahedron. Surprisingly, these algebras occurred in the classification of all algebras of generalised quaternion type, but are not weighted surface algebras. We prove that a higher tetrahedral algebra is periodic if and only if it is non-singular.

Citations

• Weighted Surface Algebras

Cited by

• A note on spherical algebras

Related

• Higher Spherical Algebras
• Local structure of tame symmetric algebras of period four
• Tame symmetric algebras of period four
• Weighted Surface Algebras
• Algebras of generalized quaternion type