Affine zigzag algebras and imaginary strata for KLR algebras

Kleshchev, Alexander; Muth, Robert

doi:10.1090/tran/7464

Affine zigzag algebras and imaginary strata for KLR algebras
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by Alexander Kleshchev and Robert Muth PDF

Trans. Amer. Math. Soc. 371 (2019), 4535-4583 Request permission

Abstract:

KLR algebras of affine $\texttt {ADE}$ types are known to be properly stratified if the characteristic of the ground field is greater than some explicit bound. Understanding the strata of this stratification reduces to semicuspidal cases, which split into real and imaginary subcases. Real semicuspidal strata are well understood. We show that the smallest imaginary stratum is Morita equivalent to Huerfano-Khovanov’s zigzag algebra tensored with a polynomial algebra in one variable. We introduce affine zigzag algebras and prove that these are Morita equivalent to arbitrary imaginary strata if the characteristic of the ground field is greater than the bound mentioned above.

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