Affine zigzag algebras and imaginary strata for KLR algebras
Affine zigzag algebras and imaginary strata for KLR algebras
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DOI：
10.1090/tran/7464
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发表时间：
2015-11
影响因子：
1.3
通讯作者：
A. Kleshchev;R. Muth
中科院分区：
文献类型：
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作者：
A. Kleshchev;R. Muth
KLR代数的仿射ADE \texttt {ADE}型是已知的适当分层，如果特征的地面领域是大于一些明确的界限。理解这种分层的层次简化为半尖状的情况，它分为真实的和想象的子情况。真实的半尖状地层是很好理解的。我们证明了最小虚层是Morita等价于Huerfano-Khovanov之字形代数张量的多项式代数在一个变量。我们引进仿射Z字形代数，并证明了这是森田等价于任意虚地层，如果地面场的特征是大于上述的界限。
KLR algebras of affine ADE \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.