We construct an odd version of Khovanov’s arc algebra Hn. Extending the center to elements that anticommute, we get a subalgebra that is isomorphic to the oddification of the cohomology of the (n,n)-Springer variety. We also prove that the odd arc algebra can be twisted into an associative algebra.
Dos Santos Santana Forte Vaz, P., & Naisse, G. (2017). Odd Khovanov’s arc algebra. Fundamenta Mathematicae, 241, 1-36. https://doi.org/10.4064/fm328-6-2017 (Original work published 2017)