An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2

Jesse Cohen

doi:10.4064/fm230712-2-12

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arXiv · 2209.01705

An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2

Jesse Cohen

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Abstract

We show that there is an associative algebra $\widetilde{H}_n$ such that, over a base ring $R$ of characteristic 2, Khovanov's arc algebra $H_n$ is isomorphic to the algebra $\widetilde{H}_n[x]/(x^2)$. We also show a similar result for bimodules associated to planar tangles and prove that there is no such isomorphism over $\mathbb{Z}$.

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BibTeX RIS

Jesse Cohen. 2022-09-04. An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2. https://doi.org/10.4064/fm230712-2-12

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