Author:
Erdmann Karin,Skowroński Andrzej
Abstract
AbstractWe introduce a new class of symmetric algebras, which we call hybrid algebras. This class contains on one extreme Brauer graph algebras, and on the other extreme general weighted surface algebras. We show that hybrid algebras are precisely the blocks of idempotent algebras of weighted surface algebras, up to socle deformations. More generally, for tame symmetric algebras whose Gabriel quiver is 2-regular, we show that the tree class of an arbitrary Auslander–Reiten component is Dynkin or Euclidean or one of the infinite trees $$A_{\infty }, A_{\infty }^{\infty }$$
A
∞
,
A
∞
∞
or $$D_{\infty }$$
D
∞
.
Publisher
Springer Science and Business Media LLC
Reference24 articles.
1. Assem, I., Simson, D., Skowroński, A.: Elements of the Representation Theory of Associative Algebras 1: Techniques of Representation Theory, London Mathematical Society Student Texts, vol. 65. Cambridge University Press, Cambridge (2006)
2. Benson, D.J.: Representations Cohomology. I. Basic Representation Theory of Finite Groups and Associative Algebras. Cambridge Studies in Advanced Mathematics, vol. 30. Cambridge University Press, Cambridge (1991)
3. Bialkowski, J., Erdmann, K., Hajduk, A., Skowroński, A., Yamagata, K.: Socle equivalences of weighted surface algebras. J. Pure Appl. Algebra 226 no. 4, Paper No. 106886, 31 p. (2022)
4. Crawley-Boevey, W.: On tame algebras and BOC’s. Proc. Lond. Math. Soc. 56, 451–483 (1988)
5. Springer Lecture Notes in Mathematics, 1428;K Erdmann,1990
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献