仿射之字形代数与 KLR 代数的虚层
表示论
2017-06-21 v3 量子代数
摘要
已知当基域特征大于某个显式界限时，仿射 ADE 型的 KLR 代数是恰当分层的。理解此分层的层可归结为半尖点情形，后者分为实子情形和虚子情形。实半尖点层已被充分理解。我们证明最小的虚层 Morita 等价于 Huerfano-Khovanov 的之字形代数与单变量多项式代数的张量积。我们引入仿射之字形代数，并证明当基域特征大于上述界限时，这些代数 Morita 等价于任意虚层。
引用
@article{arxiv.1511.05905,
title = {Affine zigzag algebras and imaginary strata for KLR algebras},
author = {Alexander Kleshchev and Robert Muth},
journal= {arXiv preprint arXiv:1511.05905},
year = {2017}
}
备注
Includes new section developing the theory of affinization for general symmetric algebras, of which affine zigzag algebras are treated as a special case. Supplementary details and some minor corrections in other sections have been incorporated as suggested by referee