# On the dimension of the Fomin-Kirillov algebra and related algebras

14 Jan 2020 Bärligea Christoph

Let $\mathcal{E}_m$ be the Fomin-Kirillov algebra, and let $\mathcal{B}_{\mathbb{S}_m}$ be the Nichols-Woronowicz algebra model for Schubert calculus on the symmetric group $\mathbb{S}_m$ which is a quotient of $\mathcal{E}_m$, i.e. the Nichols algebra associated to a Yetter-Drinfeld $\mathbb{S}_m$-module defined by the set of reflections of $\mathbb{S}_m$ and a specific one-dimensional representation of a subgroup of $\mathbb{S}_m$. It is a famous open problem to prove that $\mathcal{E}_m$ is infinite dimensional for all $m\geq 6$... (read more)

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