We 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 \(A_{\infty }, A_{\infty }^{\infty }\) or \(D_{\infty }\).

中文翻译：

---

混合代数

我们引入一类新的对称代数，我们称之为混合代数。此类包含一个极端的布劳尔图代数，以及另一种极端的一般加权表面代数。我们证明，混合代数正是加权表面代数的幂等代数块，直到底部变形。更一般地，对于 Gabriel quiver 为 2-正则的驯服对称代数，我们证明任意 Auslander-Reiten 分量的树类是 Dynkin 或 Euclidean 或无限树之一\(A_{\infty }, A_{\infty }^{\infty }\)或\(D_{\infty }\)。