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arXiv:1405.6441 [math.RT]AbstractReferencesReviewsResources

Affine cellularity of BLN-algebras

Weideng Cui

Published 2014-05-26, updated 2014-11-18Version 4

We show that the BLN-algebra, which was introduced by McGerty, is affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals are generated by idempotents. This particularly implies that the global dimension of BLN-algebras is finite. For affine type $A$, thus we obtain that the affine $q$-Schur algebra $\mathfrak{U}_{D,n,n},$ when $D< n,$ is affine cellular and has finite global dimension.

Comments: We add the idempotence of affine cell ideals inspired by Nakajima, which implies that BLN-algebras have finite global dimension. Thanks to the referees' pertinent suggestions, I re-write the whole manu in my own way according to my understanding, and I am very sorry for my previous mistakes!
Categories: math.RT, math.QA
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