ALGEBRAS OF GENERALIZED DIHEDRAL TYPE

We provide a complete classification of all algebras of generalized dihedral type, which are natural generalizations of algebras which occurred in the study of blocks of group algebras with dihedral defect groups. This gives a description by quivers and relations coming from surface triangulations.

Two-color Soergel Calculus and Simple Transitive 2-representations

In this paper, we complete the ADE-like classification of simple transitive 2-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag algebras of ADE type to give an explicit construction of a graded (non-strict) version of all these 2-representations.Moreover, we give simple combinatorial criteria for when two such 2-representations are equivalent and for when their Grothendieck groups give rise to isomorphic representations.Finally, our construction also gives a large class of simple transitive 2-representations in infinite dihedral type for general bipartite graphs.