Representation Type of Finite Quiver Hecke Algebras of TypeA(1)ℓfor Arbitrary Parameters

We give Erdmann–Nakano type theorem for the finite quiver Hecke algebras RΛ0(β) of affine type |$A^{(1)}_{\ell }$|⁠. Note that each finite quiver Hecke algebra lies in one-parameter family, and the original Erdmann–Nakano theorem studied the finite quiver Hecke algebra at a special parameter value. We study the general case in our paper. Our result shows, in particular, that their representation type does not depend on the parameter. Moreover, when the parameter value is nonzero, we show that finite quiver Hecke algebras of tame representation type are biserial algebras.