Representation type of finite quiver Hecke algebras of type A⁽¹⁾_ℓ for arbitrary parameters

2013/11/19 by Susumu Ariki, Ariki, Susumu, Kazuto Iijima +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1311.4677

openalex publication_date 2013/11/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We give Erdmann-Nakano type theorem for the finite quiver Hecke algebras R^Λ₀(β) of affine type A⁽¹⁾_ℓ. 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.

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