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2015•Transactions of the American Mathematical SocietyOpen access

Representation type of finite quiver Hecke algebras of type $D^{(2)}_{\ell +1}$

Susumu Ariki, Euiyong Park

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Abstract

We give an Erdmann-Nakano type theorem for the finite quiver Hecke algebras $R^{\Lambda _0}(\beta )$ of affine type $D^{(2)}_{\ell +1}$, which tells their representation type. If $R^{\Lambda _0}(\beta )$ is not of wild representation type, we may compute its stable Auslander-Reiten quiver.

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We give an Erdmann-Nakano type theorem for the finite quiver Hecke algebras $R^{\Lambda _0}(\beta )$ of affine type $D^{(2)}_{\ell +1}$, which tells their representation type. If $R^{\Lambda _0}(\beta )$ is not of wild representation type, we may compute its stable Auslander-Reiten quiver.

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Available abstract

We give an Erdmann-Nakano type theorem for the finite quiver Hecke algebras $R^{\Lambda _0}(\beta )$ of affine type $D^{(2)}_{\ell +1}$, which tells their representation type. If $R^{\Lambda _0}(\beta )$ is not of wild representation type, we may compute its stable Auslander-Reiten quiver.

Key concepts: Quiver, Mathematics, Type (biology), Pure mathematics, Affine transformation, Representation (politics), Lambda, BETA (programming language)

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