Socle equivalences of weighted surface algebras
Abstract
We describe the structure and properties of the finite-dimensional symmetric algebras over an algebraically closed field $K$ which are socle equivalent to the general weighted surface algebras of triangulated surfaces, investigated in Erdmann and Skowroński (J. Algebra 544:170-227, 2020). In particular, we prove that all these algebras are tame periodic algebras of period 4. The main results of this paper form an essential step towards a classification of all symmetric tame periodic algebras of period 4.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.12923
- arXiv:
- arXiv:2006.12923
- Bibcode:
- 2020arXiv200612923B
- Keywords:
-
- Mathematics - Representation Theory;
- 16D50;
- 16E30;
- 16G20;
- 16G60
- E-Print:
- 26 pages