An oddification of Khovanov's arc algebras

Abstract

In this master thesis we construct an oddification of the rings $H^n$ from arXiv:math/0103190 using the functor from arXiv:0710.4300 . This leads to a collection of non-associative rings $O{H}_C^n$ where $C$ represent some choices of signs. Extending the center up to anti-commutative elements, we get a ring $OZ(O{H}_C^n)$ which is isomorphic to the oddification of the ring cohomology of the $(n,n)$-Springer variety from arXiv:1203.0797 .

arXiv commentThis master thesis is written in French but there is an English summary at the beginning of it