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Journal Article

Affine zigzag algebras and imaginary strata for KLR algebras

MPS-Authors
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Kleshchev,  Alexander
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1090/tran/7464
(Publisher version)

Fulltext (public)

arXiv:1511.05905.pdf
(Preprint), 562KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Kleshchev, A., & Muth, R. (2019). Affine zigzag algebras and imaginary strata for KLR algebras. Transactions of the American Mathematical Society, 371(7), 4535-4583. doi:10.1090/tran/7464.


Cite as: http://hdl.handle.net/21.11116/0000-0004-A79A-2
Abstract
KLR algebras of affine 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.